tutorial xflr5 tutorial

8/20/2019 TUTORIAL Xflr5 Tutorial

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Guidelines for XFLR5 v6.03 1/71February 2011

Analysis of foils and wingsoperating at low Reynolds numbers


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TABLE OF CONTENTS

1 PURPOSE ................................................................................................................................................................ 4

2 INTRODUCTION ......................................................................................................................................................... . 4

2.1 Code limitations and domain of validity ......................................................................................................... 4

2.2 XFLR5's development history .................................................................................................... .......... ......... 4

2.3 Changes introdued in XFLR5 v! ................................................................................................................ . 5

2.4 Code struture ...................................................................................................................................... ....... !

3 FOIL ANALYSIS AND DESIGN MODES ............................................................................................................................. 7

3.1 "eneral ................................................................................................................................................. ........ #

3.2 $iret %nalysis &per( ......................................................................................................................... .......... #3.2.1 Foil o)*et ............................................................................................................................................................................................. #3.2.2 Foil +odifiat ion ........................... ............................. ............................ ............................ ............................ ..................... ...... ....... ..... #

3.2.3 %nalysis,-olar o)*et ............................ ............................ ............................. ............................ ............................ ...................... ....... .. 3.2.4 perating -oint /p-oint0 o)*et ......................................................................................................................................................... 3.2.5 XFoil analysis .......................... ............................ ............................ ............................ ............................. ........................... ...... ....... .... 3.2.! XFoil errors ......................... ............................. ............................ ............................ ............................ ............................. ............. ..... 13.2.# ession eample $iret %nalysis .......................... ............................ ............................. ............................ ............................ ...... ... 1

3.3 Full 6nverse $esign &+$7( and +ied 6nverse $esign &8$7( ................................................................. 113.3.1 "eneral ............................................................................................................................................................................................... 113.3.2 ession eample Full 6nverse $esign .......................... ............................. ............................ ............................ ........................ ...... 113.3.3 ession eample +ied 6nverse $esign ........................... ............................ ............................ ............................. .................. ...... . 11

3.4 Foil $iret $esign ........................................................................................................................................ 113.4.1 "eneral ............................................................................................................................................................................................... 113.4.2 9:splines main features ..................................................................................................................................................................... 123.4.3 pline -oints main features ........................... ............................ ............................. ............................ .......................... ....... ...... ....... 123.4.4 Leading and trailing edge .................................................................................................................................................................. 123.4.5 utput preision ................................................................................................................................................................................ 12

3.4.! $igitali;ation ............................ ............................ ............................ ............................. ............................ ............................ ........ ...... 12

4 3D ANALYSIS ....................................................................................................................................................... 13

4.1


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4.3.11 Control analysis -olar >ype 5 and >ype ! ............................ ............................ ............................ ............................ ............... ..... 4!4.3.12 6nterpolation of the XFoil:generated -olar +esh .......................... ............................ ............................. .......................... ....... ...... ... 4!4.3.13 treamlines ......................... ............................ ............................. ............................ ............................ ........................ ...... ....... ...... . 4#4.3.14 Comparison to eperimental results .......................... ............................ ............................. ............................ ............... ....... ...... ..... 44.3.15 Comparison to Aind tunnel data ......................... ............................ ............................ ............................. ............................ ............. 44.3.1! Comparison to +iare and %?L results ........................... ............................ ............................. ............................ ........... ....... ....... .. 54.3.1# ession eample heory ......................... ............................ ............................ ............................. ............................ ............................ ............ ...... ....... . 554.4.3 Frames of referene ........................ ............................. ............................ ............................ ............................ ......................... ....... .. 554.4.4 Coordinates= position= veloity= and rotation vetor ......................... ............................. ............................ ......................... ....... ...... ... 5!4.4.5 Flight onstraints ........................... ............................ ............................ ............................ ............................. ...................... ....... ...... . 5!4.4.! tate desription .......................... ............................ ............................. ............................ ............................ ............................ .......... 5#4.4.# %nalysis proedure ........................... ............................ ............................ ............................ ............................. ........................... ...... 5#4.4. 6nput 54.4. utput ................................................................................................................................................................................................. !4.4.1 ession eample ta)ility analysis ........................... ............................ ............................ ............................. ..................... ...... .... !5

5 CODE SPECIFICS ..................................................................................................................................................... 67

5.1 XFoil= %?L and XFLR5 ................................................................................................................................ !#

5.2 Files and Registry ............................................................................................................................ .......... . !#

5.3 hortuts ..................................................................................................................................................... !#

5.4 +ouse input .......................................................................................................................... ...................... !#

5.5 +emory ................................................................................................................................................... .... !

5.! 7port ptions ............................................................................................................................... .......... ... !

5.# 9ugs ............................................................................................................................................................ !

5. pen oure $evelopment .................................................................................................................. ....... !

6 CREDITS .................................................................................................................................................... .......... . 69

7 REFERENCES ........................................................................................................................................ .......... ....... 70


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1 PURPOSE

This document is not intended as a formal help manual, but rather as an aid in using XFLR5. Its purpose is to explain themethods used in the calculations, and to provide assistance for the less intuitive aspects of the software.

2 INTROU!TION

2"1 !ode limitations and domain of #alidity

Lie the original XFoil, this pro!ect has been developed and released in accordance with the principles of the "#L.

$mong other things, one important point about "#L is that%

&This program is distributed in the hope that it will be useful, but 'IT()*T $+ '$RR$+T- without even the implied warrantof /0R1($+T$2ILIT or FIT+033 F)R $ #$RTI1*L$R #*R#)30. 3ee the "+* "eneral #ublic License for more details.&

T$e %ode $as been intended and written e&%lusi#ely for t$e design of model sailplanes' for w$i%$ itgi#es reasonable and %onsistent results" T$e %ode(s use for all ot$er purpose' espe%ially for t$edesign of real si)e air%raft is strongly disappro#ed"

2"2 *+,R-(s de#elopment $istory

The primar purposes for the development of XFLR5 were to provide%

− $ user4friendl interface for XFoil− $ translation of the original F)RTR$+ source code to the 1166 language, for all developers who might have a

need for it

This was done in accordance with, and in the spirit of, /ar 7rela8s and (arold oungren8s highl valuable wor, which the havebeen ind enough to provide free of use under the "eneral #ublic License.

The resulting software is not intended as a professional product, and thus it does not offer an guarantees of robustness,accurac or product support. It is merel a personal use application, developed as a hobb, and provided under "#L rules for useb all.

For this reason, it should be noted and understood that XFLR5 ma not be default4free. 3ome significant bugs affecting resultprecision have been reported in the beta releases and corrected.(owever, XFLR5 has been thoroughl tested against other software and published experimental results, up to now with somesuccess, and this permits a limited amount of trust in the results it provides.

The algorithms for foil analsis implemented in XFLR5 are exactl the same as those of the original XFoil code, except for thetranslation from F)RTR$+ to 1. +o changes nor amendments have been made. The translation in itself could have caused newbugs. (owever, the code has been thoroughl tested against numerous original XFoil analses, alwas with consistent results. Itma be found, in some cases, that one of the two programs ma not converge where the other will, or that the path toconvergence is different from one to the other. This is due to the different manner in which floating point numbers andcalculations are processed b the two compilers. (aving said this, the converged results are alwas close, and an differenceswithin the convergence criteria set in the XFoil source code.(ence, both XFoil and XFLR5 results of airfoil analsis will be referred to herein as &XFoil results&.


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'ing analsis capabilities have been added in version 9.::. Initiall, this was done at the suggestion of /atthieu 3cherrer, whohas experimented with his /athlab &/iarex& code the application of the +on4linear Lifting Line Theor ;herein referred to as&LLT&< to the design of wings operating at low Renolds numbers.

Later on, the necessit arose to add the =ortex Lattice /ethod ;herein referred to as &=L/&< for the design and analsis of wingswith geometries not consistent with the limitations of the LLT.

=ersion v>.:: introduced ?at@ and #lotinAs recommended =L/ method based on Buadrilateral rings, and the =L/ calculation of

planes with elevator and fin.)n /arch >Cst, 9::D, XFLR5 has become an )pen 3ource 7evelopment #ro!ect hosted b 3ourceforge.net.

=ersion vE.:: introduces a >7 panel method for wings and planes, including modeling options for fuselages.

*p to this last version, XFLR5 has been developed specificall for 'indows, using /icrosoft8s /F1 libraries. This is a limitation ofthe product, maing it non available for *nix, Linux, and /$1 sstems. It has therefore been decided to re4write the code usingthe cross4platform tE libraries provided b +oia. This version has been released as XFLR5 v5. It does not offer an newfunctionalit compared to the original code.

Released in a beta version in 3eptember 9:C:, XFLR5 vG introduces the stabilit and control analsis, and a modification of the>74panel method for the plane.

2". !$anges introdu%ed in *+,R- #/

#roblem si@e

The maximum acceptable si@e for mesh definitions has been increased from 9::: panels to 5::: panels max.

3ince the memor allocation increases as the sBuare power of the problem si@e, this new version will reserve more memor atthe program launch, and ma tae longer to start on those computer with low R$/.

3tabilit and control analsis

&1ontrol polars& have been replaced b &stabilit polars&, with evaluation of stabilit and control derivatives.

2atch calculations

It is now possible to run a batch calculations for a list of airfoils.

>7 panel method

The >7 panel method is now processed differentl for single wings and for planes.

For the analsis of single wings, the full >7 method is available as in v5, with the wings represented as thic surfaces withuniform doublet and source distribution.

For planes, the full >7 method has been replaced in vG b a mix formulation of >7 panels for the fuselage, and thin surfaces forthe wings.

Inertia estimations

In the inertia evaluation of wings, the mass of each strip is distributed along the strip proportionall to the foils thicness, and is nolonger concentrated at the Buarter4chord position.

2"0 !ode stru%ture

Five different &$pplications& have been implemented%

− Two direct design modes which are convenient to compare foils, and to design new foils with the use of 243plines− The mixed inverse ;703< and the full inverse ;/703< foil design routines, virtuall unchanged from the original− The foil direct analsis routines ;)#0R


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− The wing, plane and bod design and analsis


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. +OI, ANA,SIS AN ESIN 3OES

."1 eneral

This part of the code is built around XFoil and its main features, i.e. the design routines, and the direct and inverse analsis;)#0R, /703, "703, and 703


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0xperience shows, and XFoil advises, that refinement of the foil8s panels, after it has been loaded or modified, is usuall aprudent measure to tae before an analsis.

>.9.> $nalsis#olar ob!ect

*nlie XFoil, an analsis of a given foil ma be performed onl after a 8polar ob!ect8 has been defined and associated to this foil.The results of the analsis will automaticall be associated and added to the polar ob!ect.

$n number of polars ma be created and associated to a given foil.

$ polar ob!ect is defined b%

− its Tpe− its Renolds and /ach numbers− the laminar to turbulent transition criterion− the forced trip locations on top and bottom surfaces

2 default, the transition number is set to , and the trip locations are set at the trailing edge.

In addition to the Tpe C, 9 and > polars which are unchanged from XFoil, Tpe E polars have been introduced, showing data fora given angle of attac at variable Re. The purpose is to enable determination of the critical Re value.

+igure 1 6 Tpe C foil polars

>.9.E )perating #oint ;)p#oint< ob!ect

$n operating point of a given foil is defined b its angle of attac and its Re number. $lwas associated to a foil and to a #olarob!ect, the )p#oint stores the inviscid and viscous results of the analsis.

$n number of )p#oints ma be stored in the runtime database, the onl limitation being computer memor. )p#oints ma usesignificant memor resources.

To insure consistenc, an modification to the foil or to the polar causes the operating point to be deleted from the database.


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+igure 2 6 1p calculation

>.9.5 XFoil analsis

0ach time an XFoil direct analsis is performed and the convergence is achieved, an )p#oint is generated and the values ofinterest are stored in the currentl selected polar ob!ect. 7ata is added to the polar, whether the option to store )p#oints hasbeen activated or not.

$n XFoil calculation performed at the same angle of attac and Re as an existing )p#oint causes the latter to be replaced, andthe polar data to be updated.

The &Init 2L& checbox is the eBuivalent of the &Init& menu command in XFoil, i.e., it resets the boundar laer to standard valuesbefore an analsis. It is recommended to chec the box at the time of the first calculation, and whenever the analsis of an)p#oint is unconverged or is ver different from the previous one.

In the case of seBuential analsis, the &Init 2L& is automaticall deactivated after a first converged point has been reached, and isreset after an unconverged calculation.


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>.9.G XFoil errors

"iven the complexit and difficult of a viscous analsis, XFoil is remarabl robust and consistent. It ma happen however thatthe following error message is generated during an analsis.

+igure . 7 XFoil 0rror /essage

This error message is usuall caused b a too coarse paneling of the foil, or a too sharp leading edge. It is possible that in such a

case XFoil gets &stuc& and fails at an attempt to perform a new analsis. The menu command &)perating #ointReset XFoil&can be used to reinitiali@e all the variables and reset the currentl selected foils and polars.

>.9.D 3ession example J 7irect $nalsis

C. Load a foil from a file

9. K)ptional *se the M7erotateN and M+ormali@eN commands to respectivel align the mean chord with the x4axis and to setits length to C.

>. K)ptional *se the &Refine Locall& or &Refine "loball& commands to optimi@e the foil8s panels

E. *se the &7efine $nalsis#olar& command in the #olar menu, or FG, to define an analsis J for instance a Tpe Canalsis at Re O C::,::: and /ach O :.:

5. 7efine an angle of attac or a lift coefficient to anal@e J for instance α O :P

G. 1lic on the &$nal@e& button in the right toolbar to launch an analsis

D. If the XFoil analsis has converged, the 1p distribution will be displaed automaticall

Q. 1hec the 3how 2L or 3how #ressure buttons to visuali@e either distribution

. 1hec the &3eBuence& button in the right toolbar

C:. 7efine the min and max angles for the analsis J for instance from α O 4GP to α O C:P

CC. 3ince the new start value is significantl different from the last calculation ;i.e. α O :P. 1lic on the &$nimate& button to visuali@e modifications of the boundar laer or pressure distributions with angle ofattac variations

CE. 1lic on the olars& command in the =iew menu, or tpe FQ

C5. *se the mouse button and wheel to drag and @oom the graphs


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.". +ull In#erse esign 43ES5 and 3i&ed In#erse esign 48ES5

>.>.C "eneral

2oth design modes are unchanged from the original.

Foils generated b the Full Inverse method are defined b 955 coordinate points, which is excessive for subseBuent 7irect

$nalsis. $ re4paneling of the foil is strongl recommended. $lthough foils generated b the /ixed Inverse /ethod have the same number of panels as the original foil, a re4panel is stilladvisable.

>.>.9 3ession example J Full Inverse 7esign

C. 3witch to the Full Inverse $pplication ;/enu command or 1trl6><

9. 3elect a foil from the loaded database, or load a foil from a file

>. 1lic on the &+ew 3pline& button in the right toolbar dialog

E. 3elect two points either on the upper or lower surface, but not one on each

5. 7rag the spline8s control points to define a new speed distribution

G. 1lic on the &$ppl& button to register the changeD. 1lic on the &0xecute& button to calculate the new foil geometr

Q. *se the mouse buttons and wheel to drag and @oom the graph and the foil

. Repeat the process until the desired geometr is reached

C:. To store the modified foil, clic on the arrow in the top toolbar, or select &3tore foil in the database& in the Foil menu

CC. 3witch to the 7irect $nalsis $pplication ;/enu or 1trl65<

C9. *se &Refine globall& in the 7esign menu to generate a coarser panel

C>. #roceed with the direct analsis

>.>.> 3ession example J /ixed Inverse 7esign

3teps C to G are identical to the Full Inverse design method

D. 1lic on the &/ar for /odification& button to define which part of the foil is to be modified

Q. 1lic on the &0xecute& button to calculate the new foil geometr

. 1hec for convergence in the text windowIn the case of non4convergence, it is possible either to resume iterations b clicing again the &0xecute& button, or toexport the modified geometr as it is

Finish as with the Full Inverse design method.

."0 +oil ire%t esign

>.E.C "eneral

$ crude design module has been included in XFLR5, which allows the design of Foils either from 243plines or from &3plined#oints&. The former gives smoother surfaces, the latter authori@es greater control over the geometr.

This design mode however is not the best wa to design foils, and the other possibilities derived from XFoil are far more adaptedand recommended i.e.%

− modification of a foil8s thicness and camber


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− interpolation of foils− inverse methods

This foil design mode, however, ma be useful to overla different foils and compare their geometries.

$n option has been added in vG to load a bacground image, with the idea of digitali@ing existing foils.

>.E.9 24splines main features

*pper and lower surfaces are each determined b a separate and single 243pline.

3pline degree can be set between 9 and 5.

>.E.> 3pline #oints main features

*pper and lower surfaces are each determined b a set of control points

1ontrol points are lined b >rd degree 243plines

Two intermediate control points are added to the lin splines, at C> and 9> respectivel of the separation of the two controlpoints. These two points are added automaticall and are not visible, nor can the be modified

The slope at each visible control point is determined b the line passing through the immediatel previous and next control points

>.E.E Leading and trailing edge

For both methods, the slope at the leading edge is vertical and ma not be changed. In the case of a design from 243plines, thisis done b forcing the second control point to remain on the vertical axis.In the case of &3plined #oints& the slope at the trailing edge is determined b the position of two supplementar rear points, onefor each surface.

>.E.5 )utput precision

The maximum number of output points on each surface is C5:. This is consistent with the si@ing of the XFoil arras, and with the

precision reBuired for the application, although the increase of computing power and memor capacit of modern computerscould allow for more points. Tpicall, XFoil reBuires at least 5: points on each side to perform an adeBuate analsis.In both cases, it is prudent to &re4panel& the foil in the main menu, to improve the convergence of the XFoil analsis and itsprecision. This can be done with the eBuivalent of XFoil8s $+0& and &1$77& commands.*pon exit from the design module, the user is ased whether to export or not the foil to the analsis module.

>.E.G 7igitali@ation

$n option has been added in vG.:9 to load a bacground image. The purpose is to enable digitiali@ation of existing foil imagesusing splines.

$fter digitali@ation, the splines should be stored as a foil in the database, and the foil ought to be normali@ed, de4rotated and re4paneled.


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0 . ANA,SIS

0"1 9ind and body a&is' sign %on#entions

7

bod

Xbod

@wind

α

xwind

=inf

L

+igure 0 : 'ind and 2od axis

The lift and drag coefficients are given in wind axis.+ote % *p to v>.9C, calculations have been performed using a small angles approximation, which means that the wind and bodaxis were the same.

3ign 1onventions for moments J uote from 'iipedia, Flight 7namics %

“The most common aeronautical convention defines the roll as acting about the longitudinal

axis, positive with the starboard wing down. The yaw is about the vertical body axis, positive

with the nose to starboard. Pitch is about an axis perpendicular to the longitudinal plane of

symmetry, positive nose up.”

This is illustrated in the Figure 5.


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The yaw, such that the nose

goes to starboard is >0

The pitching moment

nose up is > 0

The roll, such that the

starboard wing goes down

is > 0

+igure - 7 3oment sign %on#ention


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0"2 Ob;e%t efinition

E.9.C 'ing 7efinition

+igure / 7 'ing 7efinition

The wing is defined as a set of panels. 0ach panel is defined b %

− its length li,− the root and tip chords c i and ci6C,− the leading edge offset at root and tip chords hi and hi6C− the dihedral angle δι − the mesh for =L/ analsis.

The spanwise length of a panel should be at least eBual to the minimum length of the =L/ elements on other panels. 7ivisions b@ero or non4phsical results could result from panels of insufficient length.

Twist ;washout< is processed in LLT as a modification of the angle of attac.

In =L/, the twist is processed as a modification of the wing, with the rotation center located at the Buarter chord point.*p to v>.:E, the twist has been applied as a rotation of the sections with respect to the absolute axis. From v >.:5 onwards, thesections are rotated with respect to the panelAs Buarter chord, i.e., after the panel has been rotated b the dihedral angle. Theresults are impacted for wings with panels well off the x4 plane.

The 8span8 of the wing is defined as

S=2×∑ l i


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For ease of interpretation, the wing is shown developed on a hori@ontal planform, both in the wing design dialog box and in the97 view. )nl the >7 view gives a realistic representation of the geometr.

$ wing ma be asmmetric if the foils are different on each side. This option is meant to provide some capabilit to evaluate theinfluence of flaps, but should be used with caution. It has been tested neither against experimental nor theoretical results.

E.9.9 Reference area for aerodnamic coefficients

The reference area for all wing and plane aerodnamic coefficients is the main wing8s area.

In the case of a bi4plane, the reference area is also the main wing8s area.

There reference lengths for moment coefficients are defined in SE.>.D.

Note 6

− *p to v.E.C5, the reference area and the reference span have been defined as the planform8s area and span. 'ith thisconvention, the winglets8 contribution are counted in the area and in the span. This is not necessaril the best choice,since it is usuall convenient to compare performance coefficients of a wing with and without winglets, but with aconstant reference area.

− 3tarting in vE.CG, the default option is to use the planform area and span pro!ected on the x plane. 'ith this definition,the contribution of the winglets to span and area is @ero. For convenience, it is still possible to choose either reference

area- the option can be set in the dialog box for analsis definition.

E.9.> Flaps

From version v>.CG onwards, the automatic mesh methods taes into account the breas at the flap position, if both foils at eachend of the wing panel are defined with a flap.

The recommended wa to create a flap is to define two foils at the same spanwise position, the first with a flap brea, the otherwithout. The code will ignore the @ero4length panel.

+igure < 7 Flap 7efinition

Triangular flaps, defined b a plain foil at one side of the panel and b a flap brea at the other side, are not recogni@ed.


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The flaps are counted as one for each wing side, e.g. ailerons are counted as two flaps. This is necessar to calculate separatelhinge moments for asmmetrical wings.

E.9.E 2od 7esign

The modeling of the bod is natural in a >7 panel method, but isn8t either without difficulties.

E.9.E.C /odeling options

Two options are provided, for two different purposes %

C. Representation b flat panels % this is the 8$nalsis& purpose."iven an existing bod, the idea is to digitali@e its geometr and input it in XFLR5. The resulting geometr will not besmooth, but it is usuall enough for prediction pruposes

9. Representation b 243plines % this is the &7esign& purpose.The idea is to define and optimi@e a bod geometr to achieve some targeted aerodnamic ;or cosmetic< performance.The bod points can then be exported to a text file for further use.

E.9.E.9 Importexport of bod data

To facilitate the edition process, the control points can be edited in a text file and imported in XFLR5, rather than being defined

directl in XFLR5. $n example of the format of the input file can be obtained b exporting an existing bod definition.

$ tpical format is %

H+$/02od+ameUHFR$/0xC C @CUxn n @nH)FF30TXo o o

H2)7T#0C or 9

Remars+otes %

− The ewords should be preceded b the character &H&.

− n is the number of side point definining the frame. This number must be the same for all frame. If the frames are defined withdifferent numbers of points, the frame last defined will set the number of points.

− The frames are sorted b x positions

− The points in the frame should be defined in clocwise order, on the bod8s left side, when looing at the bod from the front-this is the view which is displaed in the right panel in the bod design module.

− $ll points in a frame should have the same axial position

− The x position of a frame is defined b the first point

E.9.5 #lane 7efinition

$ plane consists in a main wing, and optionall of a secondar wing, an elevator, one or two fins, and a bod.

The bod ma be described either b cross4sections located at different streamwise locations or b +*R23 surfaces.


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E.9.5.C 3urface assemblies

The main difficult with the construction of a >7 plane model is to connect the wing, elevator, fin and bod together. 'ithout thehelp of a 1$7 sstem, it has been difficult to implement a versatile and robust algorithm, mainl because of the number ofconfigurations to consider. For instance, the elevator ma or ma not intersect the bod, it ma or ma not intersect the fin, it maintersect the bod onl on its bottom or upper surface, etc.

The onl surface verification implemented in =E.:: is a trim of the wings, elevator and fin to the bod8s surface, and even then,the algorithm ma not be robust for all configurations.

'hatAs more, even if the wings, elevator and fin are trimmed to the fuselage surface, the bod8s panels are not adapted to followtheir contour. This implies that some of the bod8s panels will be located inside the volume, which is not consistent with the paneltheor.

E.9.5.9 Tip #atches

The #anel Theor reBuires that the volume on which the analsis is performed is completel closed b the surfaces which supportthe panels. In other words, a bod or a wing cannot have an open end, in which case a numerical error will occur.

To tr to close the volumes, the code will automaticall create tip patches in the following cases %

− Left tip of the left wing, and right tip of the right wing− Top and bottom tips of fins

It will not create patches in the following cases

− "ap at the center of the wing, i.e. if the first chord is located at a positive span position− Vunction of the wing and fuselage

1aution +ote % the influence of these modeling errors on the results is unnown.

E.9.G Inertia estimations

$ calculation form is available to provide an approximate evaluation for the 1o" position and for the inertia tensor associated tothe geometr. The evaluation should not be understood as anthing else than a rough order of magnitude.

The inertia is evaluated in the default coordinate sstem, i.e. with respect to the 1o". The tensor in other sstems can becomputed b the appropriate tensor transformations.

The evaluation is based on the following assumptions.

− For the bod, the mass is distributed uniforml in the external surface, and this surface is assumed to have auniform thicness. The bod is divided in +b elementar sections along the x4axis. The weight is concentrated at thecenter of the cross section. This is illustrated in Figure Q.

− For the wings, the mass is assumed to be distributed uniforml in the wing volume along the span.In XFLR5 v5, it has been modeled as point masses concentrated at the Buarter4chord point of distributed sections alongthe span.In XFLR5 vG, it is modeled as point masses distributed both in the span and chord directions, as illustrated in .

− The mass distribution is independent of the wing8s mesh used for aerodnamic calculations-

− #arts such as actuators, batter, lead, or receiver should be modeled separatel as point masses.

+otes %

− $t this stage of the code development, the results are not used at an point in the performance calculations.The inertia evaluations are provided as a convenience for external stabilit analsis to be performed with codes such as

$=L.

− The mass defined for wings and bodies is not the one used for Tpe 9 calculations. The mass for tpe 9 isdefined with the $nalsis#olar.


19/71

#oint mass, located at the sectioncentroid, and proportional to thesection8s surface

;

4

y

+igure = 7 3ass representation for t$e body

#oint mass, proportional to

the local volume

)

&

Oy

+igure > 7 3ass representation for t$e wing

E.9.D /esh

The wing is &meshed& into a number of panels distributed over the span and the chord of the planform, and a vortex or a doubletand source is associated to each panel.

− The analsis ma be of the =L/ tpe and is performed on the mean camber line

− The analsis ma be of the >74panel tpe in which case the wing is modeled as a thic surface


20/71

It is recommended to choose a panel distribution which is consistent with the wing8s geometr, i.e. the densit of the mesh needsto be increased at geometrical breapoints and at the root and tip of the wings. $ cosine tpe distribution is recommended in thechordwise direction to provide increased densit at the leading and trailing edges.

There is a lower limit si@e for the panels below which the calculation becomes unstable, or which leads to non4phsical results.This can tpicall occur with &sine& spanwise distributions of panels. Ideall, the precision of the calculation increases with themesh8s refinement, but so do the calculation times. It is fairl simple to experiment to determine what is the best compromise for agiven design ob!ective.

+umerical instabilit ma also occur in >7 #anel analsis if a panelAs lengths in the streamwise and chordwise directions are toodifferent. The panelAs aspect ratio should be ept low.

It is possible to exclude from the calculations the wing panels with a spanwise length less than a minimum value. This can be setin the advanced settings dialog box. If the minimum length is set to @ero, then all wing panels with length less than CC::: of thespan will be excluded. This is meant to avoid numerical errors lined to small mesh elements.

#anel /ethods %

C. The current implementation uses flat Cst order panels.Ideall, these ind of panels need to have their four corners in the same plane, which is not possible for twistedgeometries. (owever, this is not seen as a ma!or issue for the low washout angles used for model sailplane wings.

9. The surface velocit is the gradient of the doublet strengths between ad!acent panels as described in ref KE. It is

therefore recommended to have the same number of chordwise panels along the span, and the same tpe of distribution,either uniform or sine.Ideall, the panels should share the same edges and corner nodes. In the case of a flap, the 8tric8 to connect properl thepanels is to define a foil with a false flap set at :P flap angle, as is illustrated in Figure C:.

+igure 1? 7 /esh disposition for a flap


21/71

E.9.D.C #anel arrangement 4 =L/ analsis

0levator =L/ #anelsmust be aligned withthe wingAs =L/#anels

1ontrol #oints

(orseshoe vortex

+igure 116 =L/ #anel arrangement for a plane

3pecial care must be taen in the disposition of =L/ panels to avoid having a control point of the tailAs surface close to the trailingleg of one of the wingAs horseshoe vortex. This would lead to a division b @ero, and inconsistent results.

)ne method to avoid this issue is to have the wing8s panels aligned with those of the elevator, .

For the same reason, it is a good idea, though not compulsor, to position fins in the planes of the wing8s panel !unctions.

E.9.D.9 #anel arrangement 4 >7 panel analsis

1hordwise panels

The 1p distribution is calculated as the derivative of the doublet strength along the panel chordwise and spanwise strips.Toachieve this, it is reBuired that each wing has a uniform number of chordwise mesh panels along the span. It is alsorecommended that the chordwise panel distribution be the same from one wing panel to the next, i.e. cosine distribution for eachwing panel. This is necessar to connect adeBuatel the mesh panels at !unctions between wing panels.

/esh panels located in flaps are not connected to the ad!acent wing panel. The remaining connections at the !unction areperformed using the method described in ref. KE.


22/71

'ae #anels

In the =L/ method, the wae is represented b the trailing legs of the horseshoe vortices.

In the >74panel method, the wae is modeled as a series of flat panels which extend 8far behind8 the wing.The idea is that each of the wing8s chordwise strip sheds a column of wae panels. The doublet strength of each panel in thiswae strip is the difference of the doublet strength of the top and bottom panels of the wing8s strip. This is a conseBuence of thefact that the wae cannot sustain load. In addition, being a thin surface, the wae panels have a @ero source strength.

The wae strips are modeled as a column of thin panels. In the simplest form, these wae panels are straight aligned behind thewing panels, as illustrated in Figure .

+igure 126 3traight wae

In a more refined and realistic implementation, the wae is aligned with the streamlines which trail behind the wing. 3ince thedoublet distribution on the wing, and the streamlines, in turn depend on the wae shape, an iteration process is reBuired to reacha converged state. This is usuall referred to as the &wae relaxation process&.

The wae relaxation is a difficult process which can easil diverge. +umerical experimentations in XFLR5 have shown that thewae panels are highl warped at the wing tips where the wae strongl rolls up on itself. The convergence reBuires close controlb the user of e parameters such as number of wae panels, length of wae panels or time steps. For these reasons, the waeroll4up process has been disabled.

The wae panels are therefore defined as flat panels which extend behind the wings trailing edges. Their length is C:: x /$1. $tthis distance, the influence of the plane8s panels is negligible.

$ difficult arises whenever one of the straight wae panels shed b a surface such as the wing, goes through another surfacesuch as the elevator, as illustrated in Figure C>a. This will lead to unrealistic, non phsical results.


23/71

In such a situation, it is necessar to modif slightl the geometr to avoid the interference Figure C>b.

+igure 1.a @ b6 9ae Interferen%e between wing and ele#ator

E.9.Q 3mmetr

$ smmetric calculation reduces the matrix8s si@e b approximatel half ;exception is the fin


24/71

+igure 10 J Influence of $spect Ratio 4 LLT 1alculation +$1$ >EC9 $irfoil 4 Taper Ratio O C 4 3weep O :P

The wing ma be computed b either one of three methods, each having its own advantages, and all having some usagerestrictions.The first is a Lifting Line method, derived from #randtl8s wing theor. The second is a =ortex Lattice method. The third is a >7panel method.The originalit of the implementations is their coupling with XFoil calculation results to estimate the viscous drag associated with

the wing, although this is done in a different manner depending on the method.

E.>.9 =iscous and inviscid calculations

In =L/ and panel methods, an inviscid analsispolar ma be defined, in which case there is no need to define a polar mesh forthe foils. The viscous characteristics will be set to @ero.

The LLT is necessaril viscous.

E.>.> Lifting Line Theor ;LLT< 4 +on Linear

E.>.>.C "eneral

The 8classic8 LLT is linear, i.e. the relation 1l O f; α < is linear, and viscous effects are not taen into account. In the presentapplication, a non4linear LLT has been implemented based on the +$1$ technical note C9G KC.


25/71

uote from Technical +ote C9G%

The hypothesis upon which the theory is based is that a lifting wing can be replaced by a

lifting line and that the incremental vortices shed along the span trail behind the wing in

straight lines in the direction of the freestream velocity. The strength of these trailing

vortices is proportional to the rate of change of the lift along the span. The trailing vortices

induce a velocity normal to the direction of the free!stream velocity. The effective angle of

attac" of each section of the wing is therefore different from the geometric angle of attac"

by the amount of the angle #called the induced angle of attac"$ whose tangent is the ratio of

the value of the induced velocity to the value of the freestream velocity. The effective angle

of attac" is thus related to the lift distribution through the induced angle of attac". %n

addition, the effective angle of attac" is related to the section lift coefficient according to

two!dimensional data for the airfoil sections incorporated to the wing. &oth relationships must

be simultaneously satisfied in the calculation of the lift distribution of the wing.

%f the section lift curves are linear, these relationships may be expressed by a single e'uation

which can be solved analytically. %n general however, the section lift curves are not linear,

particularly at high angles of attac", and analytical solutions are not feasible. The method of

calculating the spanwise lift distribution using non!linear section lift data thus becomes one ofma"ing successive approximations of the lift distribution until one is found that simultaneously

satisfies the aforementioned relationships.


26/71

In the present implementation, the non linear lift behavior is interpolated on pre4generated meshes of XFoil Tpe C polars and thenon4linearit is solved b an iteration loop %

'ing definition

3election of α, =∞ parameters

Initiali@ation of αi with the linear solution to the

LLT

Interpolation of 1l from ;α 6 αi 6 washout, Re< on

the tpe C polar mesh

1alculation of the non linear αi distribution

Loop until ∆ αi

Ycriterion

From α 6 αi 6 washout, interpolate, on the tpe C

polar mesh, values for 1d, 1m, etc.

Interpolation of 1l from ;α 6 αi 6 washout, Re< on

the tpe C polar mesh

If Tpe 9 analsis, scaling of =∞ to create a lift

opposite to the weight

If Tpe 9 analsis, scaling of =∞ to create a lift

opposite to the weight


27/71

+igure 1- 7Induced $ngle J 2i4$irfoil +$1$>EC94+$1$CEC: J $R O CE.Q J TR O 9.: J $lfa O 5P 4 =O CG.Dms

E.>.>.9 Limitations of the LLT

It is important to note that the lifting line theor has two main limitations. uote from Technical +ote C9G %

The calculations are sub(ect to the limitations of lifting line theory and should not be

expected to give accurate results for wings of low aspect ratio and large amounts of sweep

In addition, the wing8s planform is expected to lie essentiall in the X4 plane, i.e. with low dihedral.

E.>.>.> #recautions with the LLT

$s it turns out, the convergence of the non4linear LLT is not a robust process, and reBuires careful use of a relaxation factor. Thisfactor should alwas be greater than C. $ value of 9: is usuall a good start, and ma be increased as necessar forconvergence.*suall wings with low aspect ratio reBuire high relaxation value.

The number of stations across the wing span should be chosen around 9:, but ma be increased up to E:. "reater numbers donot improve the precision of the analsis, but tend to seriousl hinder the convergence. The relaxation factor should be increasedwith higher numbers of span stations.

E.>.>.E 97 vs. >7

The LLT assumes implicitl that all the surfaces lie essentiall in the X4 plane.The onl use for the sweep and the dihedral in this implementation of the LLT is for the calculation of the pitching momentcoefficient 1m.3weep and dihedral are not used in the calculation of the lift distribution.

E.>.>.5 =iscous and inviscid calculations

>here is no option availa)le to perform a non:visous LL> alulation. >he reason )ehind is that the lineartheory reBuires that a ;ero:lift angle )e defined for eah airfoil= and that there is no onvenient manner to

define this α value Ahih depends on the Reynolds num)er.


28/71

E.>.>.G Lift center of pressure

*p to v>.CC, the position of the lift center at each span location has been calculated using the usual approximation for thin airfoils,i.e. %

X CP =0.25−

Cm0

Cl

From v>.C9 onwards, the wingAs 1enter of #ressureAs x4position is calculated b interpolation of the center of pressureAs positionon the foilAs polar mesh.

For foil polar meshes generated prior to v>.:5, the foilAs center of pressure was not stored, hence the formula above is used tocalculate the wingAs center of pressure.

E.>.>.D 7ownwash

The downwash is defined at each span station as

V i=V ∞sinα i

For convenience, it is represented at the wing8s trailing edge in >7 views.

E.>.E =ortex Lattice /ethod ;=L/< 4 Linear

E.>.E.C =L/ "eneral principles

$ =L/ method has been implemented as an alternative, for the analsis of those wing geometries which fall outside thelimitations of the LLT.

The main differences from the LLT are%

− The calculation of the lift distribution, the induced angles and the induced drag is inviscid and linear i.e. it is independentof the wing8s speed and of the air8s viscous characteristics.

− The method is applicable to an usual wing geometr, including those with sweep, low aspect ratio or high dihedral,including winglets.

The principle of a =L/ is to model the perturbation generated b the wing b a sum of vortices distributed over the wing8splanform. The strength of each vortex is calculated to meet the appropriate boundar conditions ;21


29/71

+igure 1/ 7 Influence of 3weep for a given 1L 4 $ROC: 4 TROC 4 3mmetric $irfoil

E.>.E.9 Lift force and lift coefficient

The force acting over each panel is the vector cross product

F=ρ V × Γ

Γ being the vortex strength x its length,ρ is the fluid densit

= is the freestream speed'hich implies that the force is normal to each panel.

The lift coefficient is defined as

C L=

1

ρSV 2 ∑ pane ls

F wz

3 is the sum of the panelsA area, i.e. the planform8s area

Fw@ is the pro!ection on the vertical wind axis

This formula is applicable both to a chordwise strip and to the wingAs total surface.

The pitching moments and center of pressure position at each span location are calculated b summation of the lift force over the

panels.

E.>.E.> Limitations of the =L/

C. The =L/ algorithms first computes the lift coefficient 1l and the other values which ma be calculated b integration of thesurface forces, i.e. the moment coefficients and the center of pressure8s position. The viscous variables ;viscous 1d,transitions, etc< are interpolated from the value of 1l on the previousl XFoil4generated polars. This obviousl raises an issuefor high and low 1l, where the Tpe C polar curve ma be interpolated either before or after the stall angle.=L/ results should therefore not be considered around angle of attac values close to stall angles.


30/71

9. In the current formulation, the =L/ maes the assumptions of the small angle of attac. $s a main conseBuence, the trailingvortices are not aligned with the freestream velocit. This means that the influence matrix will be independent of the a.o.a.To explore this limitation, it is possible to experiment a calculation of the tilted geometr, as explained in SE.>.G.Q. Theresults tend to show that the assumption of small angles of attac is acceptable.

E.>.E.E =L/ alternative method

In the ZclassicA =L/ method, a horseshoe vortex is positioned at the panel Buarter chord and the non4penetration condition is set

at the three4Buarter chord point.

1ontrol #oints

(orseshoe vortices

+igure 1< 7 1lassic =L/ /ethod


31/71

In the method recommended b ?at@ and #lotin K>, onl the trailing vortices extend to infinit.

1ontrol #oints

uad vortices

Trailing vortices

+igure 1= 7 uad =L/ /ethod

3ince the wae must be force free, the strength of the trailing vortex is eBual to that of the trailing edge Buad vortex.

2oth methods are implemented for comparison, but give close if not identical results in most cases.

E.>.E.5 #anel disposition for =L/

The resolution of the sstem and the determination of the vortices8 strengths reBuire a matrix inversion. In some rare cases, thismatrix ma turn out to be singular due to a conflicting disposition of panels and control points on the wing8s planform.

The problem arises when a control point is positioned on the line of a vortex. This will result in a division b @ero. In those cases,manual re4paneling of the wing is sufficient to fix the problem.


32/71

1onflicting arrangement % a control point isaligned with a vortex

+igure 1> 7 uad =L/ /ethod

If inversion problems persist despite re4paneling, it will be necessar to chec the consistenc of the input data.

E.>.5 >7 #anel /ethod 4 Linear

E.>.5.C "eneral #rinciples

The >7 panel method has been implemented with the following ob!ectives %

− refine the LLT and =L/ results b a more sophisticated full >7 method, taing into account the wings8 thicness, whereas

the =L/ onl considers the mean camber line.− provide insight in the 1p distributions over the top and bottom surfaces of a wing− provide a method capable of modeling fuselages

The principle of a >7 #anel /ethod is to model the perturbation generated b the wing b a sum of doublets and sourcesdistributed over the wing8s top and bottom surfaces. The strength of the doublets and sources is calculated to meet theappropriate boundar conditions, which ma be of the 7irichlet or +eumann tpe.

$ comprehensive description of the principles of such a method is well outside the scope of this document. )nl the mainfeatures necessar to a sound use of the code are detailed hereafter. The >7 method implemented in XFLR5 is essentiall basedon the method in reference KE. For those interested, this document provides a comprehensive review of the theoretical andnumerical aspects of the method.

E.>.5.9 >7 #anel method in XFLR5 vG

In XFLR5 vG, for a >74#anel tpe, the wing8s are modeled differentl depending on whether the analsis is run for a single wingor for a full plane%

− for the analsis of a single wing, the wing is modeled as thic surface, and the full >7 method described in E is applied

− for the analsis of a plane, the fuselagebod is taen into account, and the wings are modeled as thin surfaces- this is arestriction due to the impossibilit to generate appropriate connections between wing and bod without the help of a >741$7 program.


33/71

In reference KE, the authors propose to model the circulation on the wings using uniform strength doublets, and to place the+eumann tpe boundar condition at the collocation point, i.e. the panel8s centroid or center of gravit. The alternative is to use a=L/ method, and to place a vortex at the panel8s [ chord, and the 21 point at the panel8s \ chord.

2oth method have been tested, and the second alternative has proved more precise and reliable. (ence the >74panel methodretained for planes is a mix model of uniform sourcedoublet for thic bodies, and horseshoe vortices for thin surfaces.

E.>.5.> #roblem solving

The resolution of the panel problem reBuires the inversion of a sBuare matrix of the si@e of the number of panels. This inversion isperformed b L* decomposition.

E.>.5.E 'ae roll4up

The wae roll4up process has been implemented and tested. (owever, it is not considered to be sufficientl robust to be releasedat this time, and has been disabled in vE.::.

E.>.5.5 2oundar 1onditions ;21<

In a =L/ calculation, the 21 are necessaril of the +eumann tpe, i.e. the velocit8s component normal to the surface must be@ero.

In a >74#anel calculation, the 21 ma be either of the +eumann or 7irichlet tpe. In the latter case the velocit8s potential on thepanel8s inside surface is @ero, so that the total potential inside the bod is eBual to the freestream velocit8s potential.

$fter a trial and error process, the recommendation is to use 7irichlet 21 rather than +eumann 21. The latter method is moresensitive to local geometr changes, and leads to less convincing results. This is also the choice which is implied in reference KE.The tpe of 21 can be modified in the &$dvanced 3ettings& dialog box.


34/71

E.>.5.G =alidation

Infinite 1linder and 3phere $nalsis

The theoretical values for the 1p coefficients of a bod in a uniform flow are %

4 for a clinder % 1p O C.: at the leading and trailing edges, and 1p O 4>.: at the lowest and highest points

4 for a sphere % 1p O C.: at the leading and trailing edges, and 1p O 4C.95 at the lowest and highest points

These values are calculated within C] b the >7 panel analsis.

+igure 2? 7 #ressure coefficient $nalsis J 3phere and near infinite clinder

4>.5

4>

49.5

49

4C.5

4C

4:.5

:

:.5

C

C.5

:.: :.9 :.E :.G :.Q C.:

+ear infinite 1linder

3phere

. Panel Analysis1p

xc

+igure 21 7 #ressure 1oefficient $nalsis J 3phere and near infinite clinder


35/71

'ing $nalsis

The 1p distributions calculated b >7 panel analsis for a near infinite wing, and b 97 panel analsis with XFoil areplotted in Figure 99 and in Figure 9>. There is general concordance for inviscid results.

4C

4:.Q

4:.G

4:.E

4:.9

:

:.9

:.E

:.G

:.Q

C

:.: :.9 :.E :.G :.Q C.:

'ing $nalsis

XFoil 4 Inviscid

XFoil 4 =iscous

+$1$ 9EC9

$lpha O 9.:P

Re O C:: :::

'ing $R O E:

1p

xc

+igure 22 7 #ressure 1oefficient $nalsis J +$1$9EC9

4E

4>.5

4>

49.5

49

4C.5

4C

4:.5

:

:.5

C

:.: :.9 :.E :.G :.Q C.:

'ing $nalsis

XFoil 4 Inviscid

XFoil 4 =iscous

+$1$ 9EC9

$lpha O 45P

Re O C:: :::

'ing $R O E:

xc

1p

+igure 2. 7 #ressure 1oefficient $nalsis J +$1$GE$EC:

E.>.G $nalsis considerations

E.>.G.C "eneral Limitations $s a general rule, LLT and =L/ are adapted to configurations of thin lifting surfaces, operating at small angles of attac.

The most Buestionable assumption of the wing design algorithm is probabl the use of XFoil transition results to wings with finiteaspect ratio. The 97 simulation proposed b XFoil corresponds to infinite wings, where a laminar bubble extends indefinitelalong the span. 3ome authors suggest that on span4limited wings, such bubbles will appear onl on a fraction of the planform.(owever, theories for >7 transitions are still in development and to the author8s nowledge, not giving total satisfaction et.

The method which consists in interpolating XFoil generated results is clearl an approximation with no real theoretical orexperimental bacground, but should be a reasonable approximation for wings with moderate to high aspect ratio.


36/71

The viscous characteristics will be less and less representative as the wing geometries differ from the ideal 97 Xfoil infinite wing.(ence those results for non planar geometries, low aspect ratio or high sweep should be considered with caution.

E.>.G.9 3election of an $nalsis /ethod

The LLT method should alwas be preferred if the wing8s geometr is consistent with the limitations of the theor. LLT providesbetter insight into the viscous drag, gives a better estimation of the behavior around stall conditions at high angles of attac, andis better supported b theoretical published wor.

The >7 panel method should be selected if there is interest in the 1p distribution on top and bottom surfaces, or if the bod8sinfluence should be taen into account.

=L/ analsis is preferable for all other cases.

The comparison of the 1p distribution at two span positions for different method of analsis is given in Figure 9E and Figure .

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.00 0.05 0.10 0.15 0.20

(mm)

Wing CpSup-CpInf Panel 3D

Wing Dela Cp - !"#2

Plane - Cp - $%in Su&fa'e() * 3.82 mm

+i&f,il * 15

Span * 1400 mm

'%,&/ * 180 mm

+ * 10.0

$ * 1.80

+igure 20 7 1p comparison for different analsis methods

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.00 0.05 0.10 0.15 0.20

(mm)

Wing CpSup-CpInf Panel 3D

Wing Dela Cp - !"#2

Plane - Cp - $%in Su&fa'e(

) * 66 mm

+i&f,il * 15

Span * 1400 mm

'%,&/ * 180 mm

+ * 10.0

$ * 1.80

+igure 2- 7 1p comparison for different analsis methods

E.>.G.> 1ore radius

In =L/ analsis, the velocit vector induced b a vortex is singular on the vortex line.

In a >7 panel method, the velocit vector is singular in the alignment of the panel sides.

This can create numerical errors in the analsis and in the calculations of the streamlines.


37/71

It is therefore highl recommended to set a minimal core radius, which can tpicall be of the order of magnitude of CC::: of themin mesh panel si@e, e.g. 1ore radius O C:4Gm. This is the value set b default, and it can be modified in the advanced settings.

The velocit at a point located on the vortex line, or in the alignement of a panel side, is @ero.

E.>.G.E 3ideslip

The simulation of sideslip has been introduced in XFLR5 vE.:

The order in which a.o.a. and sideslip are applied has its importance. In XFLR5, sideslip is modeled b rotating the model aboutthe @4axis, with a freestream velocit vector remaining in the x4@ plane. The resulting geometr is anal@ed using the conventional=L/ and panel methods. The advantage of this method is that the trailing vortices are in the vertical plane which contains thevelocit vector, i.e. are aligned with the x4axis of the stabilit frame.

z

x

β

.G.5 Trefft@ #lane, far field and near field analsis

The lift and induced drag ma be calculated b near field or b far field methods. The theoretical aspects are too vast to bedetailed here, but in essence the near field method consists in an integration of pressure forces on the panels, whereas the farfield method is based on the balance of the momentum on a control surface far downstream of the bod, i.e. the Trefft@ plane.

It is generall reported that the drag and lift results from near field analsis are significantl higher and less representative thanthose resulting from a calculation in the Trefft@ plane. This issue is not specific to the present implementation, but is reported foralmost all =L/ and panel codes. The implementation in the present code for the calculation of lift and drag is therefore the farfield method.

)n the other hand, far field analsis does not provide information on the pressure distribution over the strip, and no information on

the pitching moment with reference to the chord8s Buarter point. $ll the moments and the position of the center of pressure aretherefore calculated b summation on the panels.

In the current implementation of the >7panel method, it is considered that onl the wings shed a wae, and that the bod doesnot.

E.>.G.G Linear and non4linear behavior

Traditional =L/ and #anel analsis do not account for viscous effects. For model aircraft operating at a few ms however, theviscous drag is not negligible compared to the induced drag, and must therefore be estimated b an alternative mean.


38/71

In the present application, the viscous drag is estimated b interpolation of XFoil pre4generated polars, b the 1l value resultingfrom the linear >7 analsis. This assumes implicitl that the foil8s behavior on a finite wing is not ver different than on an &infiniteXFoil wing&. There is no real bacground, neither theoretical nor experimental, to support this approach, so it should be used withcaution.

$s is generall the case when transposing 97 results to >7 analsis, the estimation of viscous drag is probabl too low and malead to arguabl optimistic results.

2ecause the =L/ is linear, it does not, among other things, account properl for stall at high angles of attac, unlie, potentiall,the LLT.

+igure 2< 7 Linear and +on4Linear modeling

E.>.G.D +on4Linear Implementation

'ing definition

=L/ /esh creation

3election of α, =∞ parameters

Interpolation from 1l on the tpe C polar mesh ofthe other viscous variables =1d, transitions, etc.

If Tpe 9 analsis, scaling of =∞ and of the Γ i tocreate a lift opposite to the weight

1alculation of the 1l values from the Γ i

1reation of the vortex influence matrix and of theboundar conditions

Inversion of the matrix for the vortices strength Γ i

1alculation of the induced downwash and inducedangles in the Trefft@ plane

1alculation of the induced drag in the Trefft@ plane


39/71

E.>.G.Q Tilted "eometr J =L/ and >7 #anel $nalsisThe baseline =L/ method uses small angle approximation for the wae8s definition. 'ithin this assumption, the wae is alignedwith the bod axes %

− For =L/, the trailing legs of the horseshoe vortices are parallel to the bod8s x4axis ;Fig. C:4a7 #anel analsis, the trailing wae panels are in the x4 plane

The advantage of this approximation is its simplicit % onl one influence matrix is reBuired for all angles of attac, and the matrixinversion can be performed for all alphas simultaneousl.The disadvantage is that the horseshoe vortices or the wae panels are not aligned with the freestream velocit.

7

L

(orseshoe vortexα

x

@ =inf

BaC


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(orseshoevortex

α

x

@=inf

7

L

BbC

7

(orseshoe vortexα

x

@ =inf

L

B%C

+igure 2= 7 +ormal and Tilted geometr configurations

$ more representative approach is to align the wae with the wind axes ;4b


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$ wae model more refined than the simple straight line or flat panel can be of interest for two reasons %

− $lthough the wae carries no load and therefore has no influence on the lift coefficient, its shape affects the induceddrag value and derived coefficients

− $ flat wae is inappropriate for plane configurations with and elevator, since the downwash created b the mainwing influences the flow field around the elevator.

The shape of the wae is determined b the flowfield behind the wing, but in turn, the flow field is dependent on the wae shape.Therefore, the shape the wae taes in a constant state situation can be deduced b an iterative process, in which the waegeometr is updated ;&relaxed&< after each computation loop.

'ae mesh

The panels formulation implemented in XFLR5 is of the constant, flat panel tpe. 3pecial care must therefore be taen in thechoice for the wae panel8s si@e, to avoid excessive twisting. The panel si@e is controlled b three parameters %

− The wae8s total length

− The streamwise si@e for the first wae panel8s length

− The ratio, or progression factor, between two ad!acent panels in the streamwise direction

$s a general indicaction, it is advisable to set those parameters so that the first panel8s si@e is approximatel the same as that ofthe wing8s trailing edge panel.


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Roll4up process

Ideall, the lift and drag coefficients tend towards limit values. (owever, if no special precautions are taen, numericalexperiments show that the wae tends to roll up indefinitel on itself. This leads to highl twisted panels and to numericaldivergence.

3ince the roll4up is not a robust process, the iteration loop is limited both b the number of iterations and b a precision criterion.

3et Initial flat wae geometr.

3et up the problem forfor the current wae geometr.

3olve the problem for

Γ or µ and σ values

Relax the wae geometr.

Loop until maximumiterations is reached

1ompute *F) coefficients

+igure 2> 7 'ae roll4up iteration process

Reference K5 provides a comprehensive description of the issues related to wae roll4up.


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E.>.D /oments

$ll moment calculations in LLT are strictl in accordance with the formula of +$1$ T+C9G

In =E.::, the definition of the moments has been modified to clarif some ambiguities that existed up to v>.9C..

From =E.:: onwards, the geometric pitching, rolling and awing moments are calculated b integration of forces on the panels.For =L/ this is done at the vortex middle position, for >7 #anel analsis, the force is applied at the panel8s center.

The geometric moments are therefore the total moments applied to the wing or plane.For analsis purposes, it ma be interesting to brea down those moments in separate parts, or to isolate one specificcontribution to the total moment.

3trip /oment 1oefficients

These moments are calculated for each span position on the wing and are accessible in the )perating #oint graphs.

3oment Sign Ref" lengt$ Nature ,,T ,3 @ .:Panel

#itching

$irfoil

1m$irfoil

positivenose up

/.$.1.

/ O B 3 mac 1m

/oment of thelift forces around

the [ chord

point

The value for thepitching moment isinterpolated on thefoil8s polar mesh. It

taes into accountviscous effects

3um of the momentscreated b pressureforces on the strip8s

panels

The viscous part isignored

1m

/oment of thepressure andviscous forceswith respect to

X1mRef

Integration over thewing8s lifting line of the

strips self pitchingmoment, and of the

strip lift force2oth sweep and

dihedral are taen intoaccount

3um on all the panelsof the moments ofpressure forces

6

pitching moment ofviscous drag forces

'ing moment coefficients

3oment Sign Ref" lengt$ Nature ,,T ,3 @ .:Panel

#itching

"eom.;global<"1m

positivenose up

/.$.1.

/ O B 3 mac 1m

/oment of thepressure forceswith respect to

X1mRef

Integration of themoment over thewing8s lifting line.2oth sweep and

dihedral are taen intoaccount

3um on all the panels ofthe moments of pressure

forces

=iscous;global<

=1m

/oment of theviscous airfoil

drag forces with

respect toX1mRef

Integration of the moment over the wing8s liftingline.

$irfoil;at local

spanposition<

/oment of the liftforces around [

chord point1m interpolated on

polar C mesh

3um of the momentscreated b pressureforces on the strip8s

panels


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Rolling

"eom.;global<"Rm

positivewith the

starboardwingdown

3pan

R O B 3 b 1r


X1mRef

Integration of the lift8smoment over thewing8s lifting line.

7ihedral is not taeninto account

3um on all the panels ofthe moments of pressure

forces

awing

"eom.

;global<"m

positivewith thenose to

starboard

3pan

+ O B 3 b 1n


X1mRef

+$

3um on all the panels of

the moments of pressureforces

#rofile;global<

=m

/oment of theviscous airfoil

drag forces withrespect to the

plane O:

Integration of the moment over the wing8s lifting line

Induced;global<

Im

/oment of theinduced tangential

forces withrespect to the

plane O:

Integration of the moment over the wing8s lifting line

E.>.Q +eutral point, 1enter of pressure, 3tatic /argin

XFLR5 up to v>.C9 has provided a measure of the Buantit

SM= X CP − X CG

MAC

incorrectl labeled M3tatic /arginN, where

- X1# is the centre of pressureAs streamwise position

- X1" is the centre of gravitAs streamwise position

The conventional static margin of a wing or a plane ma be determined b an iterative process. It is the 1" position ;or momentreference position X1mRef< for which

dCm

dα =0

This is illustrated in the Figure >: where the neutral point is approximatel GD mm from the leading edge.


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+igure .? 7 'ing +eutral #oint

Illustration of the wa to use XFLR5 to position the 1" of a model sailplane are given in ref KG and KD

E.>. 0fficienc factor

The efficienc factor, referred to also as )swald8s factor, is a measure of the deviations of the wing8s induced drag from that of anoptimal elliptic loading, and is defined as

e= CL2

π . AR

. ICd

where

− 1L is the lift coefficient

− I1d is the induced drag coefficient

− $R is the wing8s $spect Ratio

The efficienc factor, also named )swald8s factor, should alwas be smaller than C. It ma happen however that this factorbecomes greater than C for numerical reasons in LLT, =L/ and >7 #anel calculations.

In LLT, this ma be corrected b increasing the precision reBuired for convergence, for instance with the following parameters %

− +umber of stations O E:

− Relaxation factor O E:

− convergence criterion O :.::C

− /ax +umber of iterations O >::

In =L/ and >7 #anels, a refinement of the panel densit in the streamwise direction is reBuired to reduce the efficienc factor tovalues less than C.


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E.>.C: 'ing )perating #oints and 'ing #olars

The presentation of results is the same as for foil analsis, i.e. each converged analsis generates an operating point and addsresults to a polar ob!ect. The definition and selection of an $nalsis#olar ob!ect is necessar to perform a calculation.

$n number of )perating #oints ma be stored in the runtime database, the onl limitation being computer memor. 'ing andplane operating points will use significant memor resources.

Tpe C and Tpe E polars are unchanged from foil analsis.

$ tpe 9 polar corresponds to a plane with a given weight operating at constant lift.

For a given angle of attac, the plane8s velocit is calculated to create a lift force opposite to the weight of the airplane%

V= 2mg ρSC l The angle of descent is

γ=arctanC d C l

and the hori@ontal and vertical speeds are respectivel

=x O =^ cos;γ <=@ O =^ sin;γ <

+igure .1 7 3peed polars based on Tpe 9 analsis

1onvergence for tpe 9 polars reBuires that the apparent angle of attac be greater than the @ero4lift angle. )therwise, no speedwhatsoever ma generate a positive lift...


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E.>.CC 1ontrol analsis J #olar Tpe 5 and Tpe G

The Tpe 5 and Tpe G control polars have been disabled in XFLR5 vG and are replaced b the Tpe D stabilit polars.

E.>.C9 Interpolation of the XFoil4generated #olar /esh

The code does not recalculate with XFoil each operating point at ever wing station and at each iteration%

− this would reBuire length 4and unnecessar4 calculations− XFoil8s convergence is too uncertain

Instead, the operating point is interpolated from a pre4generated set of Tpe C polars.

The wing calculation reBuires that a set of Type 1 foil polars be previousl loaded or generated for each of the wing8s foils.

+igure .2 7 #olar mesh ranging from Re O E:,::: to Re O >::,:::

The set of polars should cover the whole flight envelope of each point of the wing, with regard to both Renolds numbers and tothe apparent angle of attac.

If an point of the wing planform operates outside the available polar mesh, a warning message is issued in the log file. Thishappens for instance in the case of short tip chords of elliptic wings. In such a case, the &closest point& of the mesh will be used,and the operating point ma be generated and added to the current polar, if so chosen b the user.

For the interpolation process, the code uses indifferentl all available tpe C polars related to the selected foil. The user musttherefore be careful to provide onl a homogeneous and consistent set of polars.


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The interpolation process of a variable X ;X being 1l, 1d, 1m, Transition points etc.< from Kα O aoa + αi 6 washout, Re at ageometrical point # between the foils C and 9 is%

C. For the first foil, find polars C and 9 such that ReC Y Re Y Re9-if neither polar C nor 9 can be found, return on error if Re is less than all the polars8 Renolds numbers, use the polar of smallest Reif Re is greater than that of an polars8 number, use the polar of greatest Re

9. Interpolate each polar with α to get XCC and XC9-if either polar is not defined up to α, use the smallest or greatest angle available, and issue a warningif onl one polar is available, interpolate onl that polar, and issue a warning

>. Interpolate XC between XCC and XC9, pro4rata of Re between ReC and Re9

E. 7o the same for the second foil to get X9

5. Interpolate X between XC and X9, pro4rata of the position of the point between the two foils

E.>.C> 3treamlines

The streamlines are calculated from the vortices, or doublet and source, strengths each time an operating point is selected.

The calculation is incremental, in the x streamwise direction.

The streamline are initiated at the mesh panels leading edge or trailing edge, with a user defined offset in the x and @ directions.

The &Initial Length& is the first x4increment for the calculation of the streamline.

The rogression Factor& determines the length of step n6C vs. step n.

1aution note % The velocit vector is singular at the panel edges in >74#anel analsis, and on the panelAs vortex trailing line in=L/ analsis. This ma cause numerical instabilities, in cases for instance when the streamlines are reBuested to initiate exactlat the panels leading or trailing edge, or at the panel corners. $ minor x or @ offset is necessar to prevent the instabilit. The useof a core radius, which can be defined in the advanced settings, is another possibilit.


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E.>.CE 1omparison to experimental results

The code has been tested against experimental results and against other software, with consistent results. $lso, the =L/, >7 #anel and LLT algorithms in their XFLR5 implementation are totall independent, but give close results in the

linear part of the 1l vs. α plots.

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Cd

C l VLM - XFLR5

LLT - XFLR5

Naca TN1270

See! " 261#5$%&'

i-i*$oil Naca4416 - Naca4412

Sa+ " 15$%

R " 8 , TR " 2.5

Roo% /o*! " 2.67 $%# Re " 4.32M# Ma " 0.12

Ti /o*! " 1.07 $%# Re " 1.80M, Ma " 0.06

a'/o% " -4.5

+igure .. 7 1omparison to test results from +aca Tech. +ote C9D:

E.>.C5 1omparison to wind tunnel data

$n experiment has been carried out beginning of 9::Q on a model sailplane. The detailed results are given in reference K.

The following figures provide results from XFLR5 v>.9C and from vE.:. Results from v>.9C are mared as &F/e&, since the

calculation has been performed b F. /eschia.+ote % in vE.:, the lift calculation was performed b integration of pressure forces on the panels. From vE.C>, the calculation isperformed in the far field plane.

L!"# $%&'(

M()*%&(+(,# '* -&(.!$#!/, 120+3*

:.5

:.25

.

.25

.5

.#5

1.

1.25

:5 5 1

α ° )

C L

F+e+easure ?2+easure ?2Cl : ?L+2 : XFLR5D?4.Cl : -anels Aith )ody : XFLR5D?4.Cl : -anels @o 9ody : XFLR5D?4.Cl : LL> : XFLR5D?4.

+igure .0 7 #redicted lift curve vs. experimental results


50/71

D&)4 -/5)&

M()*%&(+(,# '* -&(.!$#!/, 120+3*

:.5

:.25

.

.25

.5

.#5

1.

1.25

. .25 .5 .#5 .1

CD

C L

F+e?2?2?2

Cl : ?L+2 : XFLR5D?4.Cl : -anels Aith )ody : XFLR5D?4.Cl : -anels @o 9ody : XFLR5D?4.Cl : LL> : XFLR5D?4.

+igure .- 7 #redicted drag polar vs. experimental results

P!#$6!,4 +/+(,# $%&'(

M()*%&(+(,# '* -&(.!$#!/, 120+3*

:.3

:.25

:.2

:.15

:.1

:.5

.

.5

.1

:5 5 1

α ° )

C M

F+e+easure ?2+easure ?2Cm : ?L+2 : XFLR5D?4.Cm : -anels A ith )ody : XFLR5D?4.Cm : -ane ls @o 9ody : XFLR5D?4.

+igure ./ 7 #redicted pitch moment vs. experimental results

It can be concluded that

− the =L/ is at least as reliable as the >7 panel method,

− the bod modeling does not improve the precision of the results

− both methods give reasonable estimations of values such as %• lift coefficient• @ero lift angle• pitch moment coefficient• @ero lift moment or @ero moment lift


51/71

− both methods tend to underestimate the drag, probabl the viscous part of it

E.>.CG 1omparison to /iarex and $=L results

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.02 0.04 0.06 0.08 0.10

&l - Mia*e

LXFLR5LLT

LVLM1L39a+el'

TCd

Cl

Sa+ " 2000 mm

Roo% $oil " N 3412

Ti Foil " N1410

R " 14.8

TR " 2.0

L: See " 0

+igure .< 7 1omparison to results from /iarex

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.;

0 0.2 0.4 0.6 0.8 1

C l

l - VL 3.16

l - VL 3.26l - LLT - XFLR5l - LLT - Mia*el - XFLR5 - VLM2l - XFLR5 - 9a+el

α "5.00i-i*$oil Naca3412 - Naca1410

Sa+ " 2000 mm

L: See " 5

R " 14.8 , TR " 2.0

+igure .= 7 Lift coefficient 4 1omparison to $=L and /iarex


52/71

-;.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

0 0.2 0.4 0.6 0.8 1

a i

i - VL 3.26

i - LLT - XFLR5

i - XFLR5 - VLM1

i - XFLR5 - VLM2

i XFLR5 9a+el'

α"5.00i-i*$oil Naca3412 - Naca1410

Sa+ " 2000 mm

L: See " 5

R " 14.8 , TR " 2.0

+igure .> 7 Induced $ngle vs. span 4 1omparison to $=L and /iarex

-0.020

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0 0.2 0.4 0.6 0.8 1

I n d u c e d

D r a g

! - VL 3.16! - VL 3.26


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-0.0;

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0 0.2 0.4 0.6 0.8 1

C m

A i r f o i l

cmc&4 - VL

mi*$ - LLT -XFLR5m - LLT - Mia*e

mi*$ - XFLR5 - VLM2mi*$ - XFLR5 - 9N:L

α "5.00i-i*$oil Naca3412 - Naca1410

Sa+ " 2000 mm

L: See " 5

R " 14.8 , TR " 2.0

+igure 02 7 #itching moment coefficient vs. span 4 1omparison to $=L and /iarex


54/71

E.>.CD 3ession example J 'ing $nalsis

C. Load the foil;s< which will be used to define the wing

9. In the 7irect $nalsis $pplication, clic the &Run 2atch $nalsis& command in the #olars menu, or tpe (Sif!"F6#

>. Run a batch analsis with the following parameters ;mae sure these values cover the whole flight envelope of the wingP

CG. 1lic the &$nal@e& button in the right toolbar

CD. 1hange settings if LLT convergence cannot be reached, or continue the LLT analsis after un4checing the &Init LLT&checbox

CQ. 1lic the &>7 view& command in the =iew menu

C. *se the mouse to @oom and rotate the model

9:. *se 3eBuence to calculate a complete wing8s polar

CG. 1lic on the olars& command in the =iew menu, (F%# to visuali@e the polar graphs


55/71

E.>.CQ +on convergences

!ause +i&

$ll methods The foils8 Tpe C polar meshes do not cover theavailable flight envelopeKmost usual case of non convergence

0xtend the foils8 Tpe C polar meshes

In Tpe 9 analsis, the lift is negative 1alculate onl for higher values of the angle ofattac

In Tpe 9 analsis, the speed is either too lowor too high, leading to )p#oints outside of theavailable flight envelope

0xtend the foils8 Tpe C polar mesh -The speed will tend towards infinite values at lowaoa, and smm

tutorial xflr5 tutorial

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