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1. In this example the first two words specify the same number 2 OVERVIEW OF INPUT AND GENERAL OPTIONS 2 e If the character F occurs within a DLFF word usually at the beginning of the word Subrou tine DLFF continues reading that word and that sentence in column 1 of the succeeding line Thus the continuation line has neither an alphanumeric name nor the four integer numbers e A line may contain more than one DLFF sentence A second call to Subroutine DLFF without specifying the column in which reading should begin initiates reading following the end of the preceding sentence An example of a line containing two DLFF sentences is 12 0 12 12 01 40000 1 5117 3 00368 1 The first sentence contains the four numbers 12 12 12 01 and 40000 the second the three numbers 5 7 and 3 00368 All data are input as they will be used within the code i e no multiplication factor is applied within the code An exception is the RE line in which the Reynolds numbers are specified in thousands For example RE Luuuuuuuu31000 5 1500 7 10000 which specifies Reynolds numbers of 1 000 000 500 000 and 10 000 000 with transition modes 3 5 and 7 respectively See Chap 6 3 1 2 Character Strings for Supplementing Plots Several options produce plots These plots can be supplemented by labels in several ways some of which are based on character strings contained in the input lines The characters are formed by sequence
2. j 1 j 2 5mm 2m S38 eee ee a 5mm ai 0 5mm 2mm PEA TE j ab 10mm 2mm PE 0 5mm 2mm 6 7 5 Scaling The width of the CDCL diagram is normally 379 mm This width is multiplied by a scaling factor SCF The default value of SCF is 1 If NUPA 9 and F gt 0 SCF F For example 6 BOUNDARY LAYER ANALYSIS 61 which sets SCF to 0 7 Note that only the scale is changed no plotting is performed 6 7 6 Empty Grid An empty grid plotted on a transparency is useful for the evaluation of the CDCL diagram If NUPA 9 and F lt 0 a grid with Ac 0 1 and Aca Ac 1 100 is plotted A second grid with Aces 0 5 and Acg2 Ace 2 100 is plotted to make every fifth line bolder The first grid is plotted with line width PEN AX the second with 2 x PENAX The value of PENAX can be specified in a REMO line see Chap 2 2 2 If Fy 0 Ace Fo If F3 0 Ace2 F3 6 7 7 Examples The first example plots a diagram for the NACA 23012 airfoil fig 19 The diagram remains open for the plotting of results for the same airfoil with a simple flap Because the flapped airfoil is expected to produce higher cy values the key and accordingly the frame are extended upward by F 0 6 The option with LAUF F 0 is exercised to include the explanations for the first plot as well The explanation block is included because NUPU 5 in the first CDCL line and labels are
3. 1 6 4 16 5 2 1 6 6 0 ALFA 102468 10 12 14 16 18 DPIT 27 RE 120 3 1000 CDCL 81 3 1 1With displ it DPIT 0 RE 3 1000 CDCL 82 21 0542 3311440 2 25 3 2 10 4 DPIT TEST SHO s580 1 With displ it R 3 0x10 55 2 With displ it 6 0x10 ERE 3 0x10 ices 6 0x10 Cy 0 55 10 510 Figure 25 Boundary layer summary diagram with and without displacement iteration 7 Rules for Input and Flow Chart 7 1 Input Line Sequence The following table presents an input line summary along with rules for the sequence of the input lines 7 RULES FOR INPUT AND FLOW CHART Line Must be preceded by REMO Line Must be preceded by STRK STRD TRA2 or FXPR EHNN RE ALFA FLZW ALFA TRA1 PAN Pow PIWA 70 7 RULES FOR INPUT AND FLOW CHART 71 2 Flow Chart jo ursy g A x Jojod peeds LNd LAO busy A x pa 0 5 2 3 pup 9 x buisn T3NVA JUVISVI 9 A pup 9 x OudVal Lavls REFERENCES 71 References 1 Eppler Richard and Somers Dan M A Computer Program for the Design and Analysis of Low Speed Airfoils NASA TM 80210 1980 2 Eppler Richard and Somers Dan M Supplement to A Computer Program for the Design and Analysis of Low Speed Airfoils NASA TM 81862 1980 3 Eppler Richard Airfoil Design and Data Springer Verlag Berlin 1990 4 Eppler Richard Praktische Berechnung laminarer und turbulent
4. AK If ITMOD 5 K is replaced by K AK lf IT MOD 6 K is replaced by K AK and K is replaced by K AK This option should not be used if K and K have opposite signs for example if both values are determined by RSM 2 and y and ji have opposite signs In this case the effects of AK on K are opposite for the upper and lower surfaces and the iteration may diverge or at least produce unintended results If ITMOD 7 aj is replaced by aj Ao If ITMOD 8 aj is replaced by az Ao If ITMOD 9 a is replaced by aj Aa and aj is replaced by a7 Ao In all iteration modes Aa or AK is determined such that Ky Ky Ks Kp as specified by Fy During the iteration Aa is rounded to 2 a digits and K to 3 a digits to the right of the decimal point Therefore Kg may not be exactly equal to Kp The TRA2 line initiates the design of the specified airfoil The x c and y c airfoil coordinates the inner normal angles and the velocity function v cos y 2 a are stored in blank COMMON arrays X Y ARG and VF respectively Normally the code produces two tables containing all the v values including v and their cor responding a values as well as the pressure recovery and closure contribution parameters in the first line for the upper surface and in the last line for the lower surface The first table contains the input values the second the values from the final iteration Bet
5. PLW 33 T 1C S O1SPAN W 1W A 1A Z M70 4 6 6 6 PLWA Line The PLWA line allows the wing area S the aircraft mass W and the parasite drag area A specified by the preceding PLW line to be modified Any number of PLWA lines can succeed one PLW line The effect of the modifications on the lift and parasite drag coefficients only is computed 6 BOUNDARY LAYER ANALYSIS 54 EPPLER 98 16 6 98 R 19 6 98 14 08 50 100 DO v km h 200 ll li l ll l l ak k a th Creat 110 Sy se po x x NACA 4412 12 B i sie ee 2 20 NACA 6412 12 C T EG TTN t x P SQ T ape oe x NS 37330 1 A sles x y t De wee N al S AAA E 4 40 a ee al Speed Polars Span 18m W 400kg A 12 58m 5 50 Figure 18 Speed polars of one aircraft with three different airfoils Because the lift coefficients are affected the aircraft speeds and the induced drag coefficients are also affected No influence on the Reynolds number from the altered chords and speeds is considered the profile drag coefficients from the computations initiated by the PLW line are used NUPA NUPE and NUPI specify options for plotting the speed polar as described for the PLW line NUPU NMOD which is the number of modifications AS which is the change in wing area in m AW which is the change in aircraft mass in kg 1078F AA which is the change in parasite drag area in m The code adds nAS to S nAW to W an
6. The X lines contain the z c values The Y lines contain the velocities if the preceding ALFA line has NUPI lt 1 or pressure coefficients if NUPI gt 2 The E line terminates the experimental data The X and Y lines are read by the same subroutine as are the experimental data for the CDCL diagram see Chap 6 7 Thus the same options are available The first line in the key is solid with the explanation Theory The available symbols are shown in figure 12 The following example produces the diagram shown in figure 14 REMO1 P 9US TRA1 88 0 5 60 5 TRA29 88 4 17 5 2 1 6 4 17 5 2 1 6 3000 ALFA201 2 99 9 0 DIAG 1 102 2 1 65 2 2 3 3 1 25 3 2CiPlain X 100 45 50 60 65 Y 100 135 140 135 160 2 T 1Fictitious Experiment E FLAP 250315 ALFA 1 230 DIAG 2 1 12 2 16 32 7 21 2 F 1 ZF 2 1Flap 3 1Flap The velocity distributions for two different flap deflections 0 and 15 are plotted in one diagram by means of DIAG lines with NUPU 1 and NUPU 2 The labels a are added when 7 is negative The labels Plain and 25 Flap 15 are inserted after the labels with 7 1 which occcurs once in each DIAG line The label Flap is inserted after the a labels corresponding to the second and third groups of three numbers Ficticious experimental data are included The following example produces figure 15 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES Theory x Fictitious Experi
7. a character string can be given that is added at the end of the corresponding line in the key In a line that terminates the diagram i e NUPA 1 or 3 a character string can be given after Z that is inserted at the end of the caption It should be remembered that the font for capital Greek letters see ref 6 is valid after the airfoil thickness is written and that no space is present between the thickness and the first character of the strings Thus the first string after the airfoil name should begin with a space followed by 1 or 2 to specify the desired font The caption and the key are positioned where in most cases sufficient space exists It can occur however that the caption or the key intersects the curves Therefore two options are available by which other positions can be specified as follows After L two DLFF words can be given that specify the upper left corner of the key After M two DLFF words can be given that specify the upper left corner of the caption The coordinates are given in the units of the diagram i e velocity and either sink rate sink or power The following example produces the diagram shown in figure 18 REMO11 000 3 3 FXPR 5 NACA 43012 61 40 30 12 ALFA20 1 1 3 1 6 2 2 2 2 434568 10 12 14 15 16 FLZW 3 30 60 PLW 21 3 1 400 10 05 96 76 56 T 1A FXPR 4 NACA 4412 61 04 40 12 ALFA PLW 42 T 1B FXPR 4 NACA 6412 61 06 40 12 ALFA20 1 1 3 1 6 2 2 4 263456810 12 14 15 16
8. as recommended only one displacement iteration is initiated by each F number i e e 0 or 1 no restriction applies to the RE or FLZW lines The first example plots the results of the displacement iterations for R 3 x 10 at a 2 and 8 into the diagram that remained open after the uniterated velocity distributions were plotted fig 24 Only one Reynolds number is permitted because the second F number in the DPIT line must specify plot mode mbt 3 which cannot be specified more than once Figure 24 illustrates not only the effect of the displacement iteration on the velocity distribution but also on the airfoil contour Slight irregularities in the iterated velocity distributions occur near the transition locations these also occur in experiments REMO1 P TRAIL 9 0 10 60 3 TRA26 9416 52 1 6 4 16 5 2 1 66 000 ALFA 228 DIAG 1 1 312 622 44 ALFA 90246810 12 14 16 DPIT 2 40 5 30 RE 3 3000 TE 0 0 5 x c 1 Figure 24 Effect of displacement iteration on velocity distributions In the second example the first DPIT line specifies two a values the second and the seventh i e a 2 and 12 for displacement iterations The succeeding RE line and the CDCL line with NUPU 1 initiate the diagram shown in figure 25 to which results without iteration are later added The iteration affects only the lift and moment curves 7 RULES FOR INPUT AND FLOW CHART 68 REMO1 PDPIT TEST TRA1 9010 60 3 TRA26 9416 5 2
9. have always been guided by the principle that previous data sets should still be valid For this reason some input features are not as simple as they might be 1 1 Format of Input Lines For all input lines except those containing airfoil coordinates or experimental data the first 10 columns are read using the FORTRAN format A4 311 13 Thus each line contains in columns 1 4 an alphanumeric line name in columns 5 7 three integer numbers NUPA NUPE and NUPI having one digit each in columns 8 10 one integer number NUPU having three digits and in columns 12 80 up to 22 floating point numbers referred to as F numbers F F The input reading is performed in Subroutine DLFF The following definitions apply e The symbol denotes a space Thus uuu denotes four consecutive spaces e A DLFF word is a number possibly with a minus sign and or a decimal point It may have as many digits as desired It is always read as a floating point number The decimal point at the end of the word can be omitted Leading zeroes ahead of the decimal point can also be omitted A DLFF word is terminated by a comma or a space For example 12 0 12 003 12 3456789 e A DLFF sentence consists of an arbitrary number of DLFF words separated only by a comma or a space The sentence is terminated by two columns containing either a comma and a space or two spaces For example 12 0 12 12 01 400000 003 12 0 112 112 01 400000 003
10. three numbers contain k which is the number of the MU R pair in the preceding RE line or the c O pair in the preceding FLZW line c which for the first five labels is the cy value where corner e of the label rectangle will be located near the kt curve For the last label c is the a value for corner e in which case c 0 Is not useful and therefore c 0 plots the label at the left end of the kth cm curve if e 0 and at the right end if e 1 e is the corner number see DIAG Line Chap 5 6 If e gt 0 the next group of numbers specifies the position of the next label If e lt 0 the next group numbers plots the same label in a different position Thus it is possible to plot one label in several positions The last label c a alone can be plotted only once For this label a negative e supresses the a which is occasionally necessary because of the limited space near the cm curves If k 0 the corresponding label is not plotted The values c and e can be omitted if k 0 after which the input must begin with a new DLFF sentence Its first word is the value k of the next group of three numbers Thus in this case two spaces must be input between the last word of a group and the first one of the following group If a group has three numbers the next group can follow without beginning a new DLFF sentence The corner e of the label rectangle is positioned at the lower or upper end of the kt curve if th
11. 0 a maximum aircraft speed Umax IS specified and v min ee gt PR aa 10 0 11 a 6 BOUNDARY LAYER ANALYSIS 50 The speed v is used to calculate the Reynolds number UC R 11 which therefore depends not only on the local angle of attack and aircraft mass but also on the local twist angle and the local chord Note that if a Mach number M 4 0 is specified before an FLZW line the variation of Mach number with angle of attack is considered Because the Cz also depends on the Mach number an iteration process is necessary to obtain agreement between Cz M and v Accordingly each requires three to five runs of the panel method which increases the computing time Also note that if the computation is to be performed with roughness elements they must be specified in the last RE line preceding the FLZW line This RE line must specify at least one Reynolds number Everything else is processed exactly as it is for an RE line including the print and plot modes and storage of the results NUPA NUPE and NUPI see RE Line Chap 6 3 NUPU MU which contains up to three digits a0c as defined for the RE line If MU contains only one digit it is interpreted as a two digits are interpreted as a0 All options described for the RE line are allowed Fixed transition i e a 1 or 2 requires the transition locations to be specified in the preceding RE line F W S which is the wing loading aircraft mass wing
12. 25 0 0 25 0 5 Finally the values Av 0 125 0 0625 are used according to the amount of camber near the leading edge No more than 13 points are inserted which is adequate even for very sharp leading edges It should be remembered that the airfoil points are normally computed for integer values of v 3 AIRFOIL DESIGN 10 whereas vi is computed during the design procedure and not known in advance The additional points are thus located relative to the unknown leading edge If an additional point falls too close to an integer one the integer one is omitted The value Av 0 corresponds to the airfoil point to be computed for v This is the leading edge in an aerodynamic sense At that point the airfoil has its maximum camber and its maximum suction peak This point does not necessarily however coincide with the geometric leading edge i e x c 0 As a consequence of the additional points all airfoils are defined by more points than specified in the TRA1 line This is of no concern unless the airfoil is analyzed using the panel method For example FLAP lines may cause the number of points to increase before the panel method is called Because the total number of points is restricted to 129 no more than 108 points should be specified in the design mode Due to the precise definition of the leading edge region 60 points normally yield very precise shapes The code works internally with many more points in the most critica
13. NUPE 1 are evaluated before the frame is opened and the frame is sized accordingly Without additional input the upper edge of the frame is set to V 2 5 or Cp 3 The curves 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 37 are not plotted beyond this limit The upper edge of the frame can be extended by specifying FF in a DIAG line with NUPU 0 or 1 in which case F gt specifies Viimit or Cp timit The upper edge of the frame will be extended if the limit specified by F is greater than that derived from the data This can be applied in two ways as follows If the data corresponding to the first DIAG line i e NUPU 0 or 1 exceeds the default limit V 2 5 or C 3 and the entire curves are to be plotted If following a DIAG line with NUPU 1 the curves from succeeding DIAG lines with NUPU 2 or 3 require a larger frame than those from the first DIAG line Labelling Without additional input the axes are labelled a relative to the x axis or a relative to the zero lift line and all values used for the diagram are plotted in the upper right corner The airfoil name and thickness in percent chord valid for the DIAG line terminating the diagram i e NUPU 0 or 2 are plotted inside the airfoil or if the airfoil is too thin below it If NUPU 0 and only one a value is input this value is included in the label a relative to the and the plotting in the upper right corner is omitt
14. a horizontal translation of the curves is performed If only two a values are specified for the displacement iteration the least squares fits are merely straight lines through two points If one of these points corresponds to an a at which extensive separation occurs the corresponding ce will be reduced considerably and the least squares fit will be unrepresentative of the linear portion of the lift curve It is therefore recommended that the displacement iteration be performed only for a values within the linear portion of the lift curve i e for a values at which no significant separation occurs The DPIT line must immediately precede a line initiating a boundary layer computation i e RE FLZW or PLW line NUPA NUPE NUPI and NUPU are ignored If F F5 gt 0 the F numbers specify the angles of attack for which a displacement iteration is performed and also the plot mode mbt The F are given as abc de where abc is interpreted as an integer n A displacement iteration is performed for the nth angle of attack in the preceding ALFA line and for each Reynolds number in the immediately succeeding RE FLZW or PLW line If d gt 0 a diagram containing the airfoil contour including the displacement thickness and the velocity distribution for the specified angle of attack is plotted after each displacement iteration The plot mode mbt is set to d 1 and interpreted as described under DIAG Line Chapter 5 6 and reviewed
15. airfoils If S 4 0 and N 4H 1 a different smoothing based on a compensation spline is performed once Wortmann airfoils can be smoothed using this routine if N 0 Both smoothing routines modify the airfoils as little as possible The second routine initiates a coordinate transformation exactly as NUPI 4 0 4 POTENTIAL FLOW AIRFOIL ANALYSIS 16 does The first routine may result in a point x 0 y 4 0 even though all Wortmann airfoils already have a point at x 0 y 0 An example is given at the end of Chapter 5 6 4 1 2 Insertion of Additional Points The F numbers in the FXPR line and in the PAN and FLAP lines specify additional points to be splined in between the original coordinates as read or generated following the FXPR line The F numbers F are interpreted as sab c where s is an optional minus sign and a b and c may contain more than 1 digit each See example below If ab 0 one point is inserted at z c 0 c on the upper surface or on the lower surface if s iS a minus sign If ab 0 c contains only one digit The number b contains two digits if c 4 or 5 and only one digit otherwise Then b new points are inserted between points a and a 1 If s isa minus sign b new points are inserted between points VQ a and NQ a 1 which specify the locations of the new points relative to the trailing edge This is helpful if NQ has been changed since the design or coordinate input for example by the addition of poi
16. assumed to occur at that location and de is not increased The latter effect simulates fixed transition in a wind tunnel for example The elements are specified by F numbers F F 9 F F contain five digits abb cc which are interpreted as follows labb specifies the location of the roughness element xp in percent chord If zR 0 no roughness element is introduced by that F number cc which is interpreted as 0 cc specifies the roughness height in percent chord Note that cc can have more than two digits and therefore the roughness height can be less than 0 0001c e g 0 1 mm for a chord of 1 m F and F2 specify roughness elements on the upper and lower surfaces for the first MU R pair Fiz and F 4 specify roughness elements on the upper and lower surfaces for the second MU R pair 6 BOUNDARY LAYER ANALYSIS 48 and so on up to Fig and Foo Accordingly roughness elements can be specified on either surface for each MU R pair If fewer roughness elements than MU R pairs are specified the last pair of roughness elements is used for all remaining MU R pairs Usually only one pair of roughness elements is specified which is then valid for all MU R pairs In most applications the locations of the roughness elements are the same for all wind tunnel or flight conditions F Foy are read from each RE line that specifies at least one Reynolds number The roughness elements remain in effect until an RE line with F gt 0 is r
17. below The RE FLZW or PLW line must specify only one Reynolds number if d 2 or 3 If d 1 one set of data is plotted axes are drawn and the diagram is terminated i e closed to further plotting If d 2 one set of data is plotted and the diagram remains open to further plotting If d 3 one set of data is plotted into the open diagram axes are drawn and the diagram is terminated If d 4 one set of data is plotted into the open diagram which remains open to further plotting If e 0 e displacement iterations are performed for the angle of attack specified by abc Note that e 0 and e 1 are equivalent The specification of e gt 1 is not recommended If F5 lt 0 the curvature of the displacement surface d6 da is limited to SLM 0 bcde This limit is used until it is reset by another DPIT line with F lt 0 Only four angles of attack can be specified in DPIT lines with F lt 0 The DPIT line is valid for only one airfoil A TRA2 FXPR or FLAP line invalidates the DPIT line 6 BOUNDARY LAYER ANALYSIS 67 A new DPIT line must be given if a displacement iteration is to be performed for the new or flapped airfoil An important restriction applies to the performance of multiple displacement iterations i e e gt 1 If e gt 1 is specified in one or more of the F numbers the succeeding RE line must contain only one Reynolds number similarly the succeeding FLZW line must contain only one chord If
18. containing pressure coefficients is produced NUPI gt 2 with a 2 4 6 8 and 10 relative to the x axis NUPI 3 ALFA no additional input NUPI na and the values of a from the preceding ALFA line with NUPU 0 are used and print modes mzy mcm and mpa remain as before ALFA20 NUPI Na and the values of a from the preceding ALFA line with NUPU 0 are used The moment coefficient listing and the x y V listing are not produced NUPA 2 4 0 therefore may NUPE 0 A special option lists the second derivatives of v in the x y V listing This allows the curvature of u usually in the ramp area to be checked See ref 3 If an a 4 0 and aj 41 0 the second derivative of the velocity or pressure distribution is listed for aj 1 5 6 DIAG Line The DIAG line initiates the plotting and labelling of two different diagrams the x y V diagram which contains the airfoil shape and velocity or pressure C distributions or a so called pressure envelope diagram which is relevant for cavitation on hydrofoils If NUPA 0 the lines in the x y V diagrams are plotted as polygons instead of splined curves The coordinate points in this case can be distinguished by the corners of the polygons If NUPE 1 experimental data are inserted into the x y V diagram see below NUPI determines the type of diagram to be plotted and the line type to be used see below NUPU specifies the plot mode mbt by whi
19. is 0 0001 The variable AB FA is a factor by which all v values in the TRA1 lines as well as A A A and A in the TRA2 line and Av and Ay in the RAMP line are multiplied This factor allows the number of points N to be changed for a given airfoil design for which TRA1 TRA2 and RAMP lines already exist If the final arc limit in the TRA1 line is N then N x ABFA must still be divisible by 4 4 POTENTIAL FLOW AIRFOIL ANALYSIS 14 Thus the usual number of points N 60 specified in the TRA1 line can be changed to N 108 for example by setting ABFA to 1 8 Note that if the arc limits in the TRA1 lines were selected such that they fall midway between the points on the airfoil this will no longer be true if ABFA 4 1 The value of ABFA must not be so large that the total number of points exceeds 120 EPSPA specifies e in the panel method where the subpanelling is a function of e As e decreases more subpanels are used when the induced velocity is computed at a point located very close to the panel All four values mpr NPG ABFA and e remain in effect until the next ABSZ line is read Thus a new ABSZ line with F 1 resets ABFA to its default value 4 Potential Flow Airfoil Analysis The potential flow analysis method requires only a set of airfoil coordinates which can come from the design method or from the input Because airfoil coordinates do not conveniently fit into the format used for all the other input lines they are
20. minimum cy along the cg axis is automatically shifted in steps of 0 005 There are options for additional labelling similar to those for the DIAG line The CDCL line also allows the insertion of experimental data If NUPA 1 8 the types of broken lines can be specified see below If NUPA 9 the width of the plot can be specified or an empty grid can be plotted see below Thus if NUPA 4H 0 a diagram is not plotted only the parameters for the line types or the scale factor are specified and therefore another CDCL line with NUPA 0 must be given to plot the boundary layer summary If NUPA 0 the boundary layer summary is plotted If NUPE 1 8 experimental data are read from the succeeding lines see below This option is valid only for CDCL lines that open the diagram i e NUPU 0 1 4 or 5 If NUPE 9 only experimental data are plotted The frame and the axes are specified by the F numbers see below NUPI is ignored NUPU specifies the options for plotting the results from more than one boundary layer computation in one diagram and the insertion of the explanation blocks If NUPU contains two digits ab LAU F a where if LAUF 4 0 the line types of the current MU R pairs and the labels are included in the key see below The line types for the next CDCL plot are not reset to the first line type but rather set to the next one in sequence 6 BOUNDARY LAYER ANALYSIS 56 if LAUF 9 the airfoil thickn
21. na and the values of a from the preceding ALFA line with NUPU 4H 0 are used The F where i 1 Na specify the angles of attack a in degrees If F 99 ab a az where k ab If k O ork gt na then k 1 This option allows a values from the airfoil design to be used as a Remember that the velocity over airfoil segment is constant at this a This option is useful if the values of af have been changed by iteration during the design procedure If this option is specified after an airfoil analysis or if k i lt Nna the a is skipped Internally the code uses the angle of attack relative to the zero lift line If NUPI 1 or 3 all angles of attack relative to the x axis are converted to values relative to the zero lift line and then back to values relative to the x axis for output only If the option F 99 ab is used with NUPI 1 or 3 the a are converted to values relative to the x axis for output The following examples illustrate the use of the ALFA line ALFA21 11u1111 99 99 05 3 No moment coefficients are listed mcm NUPA 2 4 1 the x y V listing containing velocities 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 35 is produced NUPA 0 and therefore may NUPE 1 NUPI 0 and a 1 ag a3 a3 ag and ay 3 all relative to the zero lift line NUPI 0 ALFA Hu 34124446 _ 8 10 Print modes mcm and may remain as previously set NUPA 0 If may 0 the x y V listing
22. of points on the circle is multiplied e The input lines for potential flow analysis are FXPR line which reads a set of airfoil coordinates and PAN line which switches from the design to the analysis mode and specifies cascades e The options for both design and analysis modes are specified in STRD and STRK lines which together plot airfoil shapes with various chords MACH line which computes compressibility effects on the velocity or pressure distribu tions FLAP line which alters the airfoil shape to that corresponding to the deflection of a simple flap or a variable geometry device ALFA line which contains the angles of attack to be analyzed DIAG line which plots velocity or pressure distributions and PUXY line which writes the airfoil coordinates to a file e The input lines for boundary layer analysis are RE line which specifies the transition modes and Reynolds numbers FLZW line which specifies the aircraft data required to compute the boundary layer de velopments for which the Reynolds number varies with aircraft lift coefficient and local chord PLW line which specifies additional aircraft data required to compute a speed or power polar PLWA line which increments the aircraft data from the PLW line CDCL line which plots the section characteristics and DPIT line which performs the boundary layer displacement iteration 2 2 General Options 2 2 1 C Line The C line specifies a comment w
23. the airfoils in the next STRK line with NUPU 4 999 Negative x are permitted The default value of x is 0 The trailing edge c Zie of the first airfoil to be plotted in a diagram determines the width of the diagram The width can also be set by a positive zie and c lt 1 mm in which case the airfoil that determines the width is not plotted The plots that exceed the width of the diagram are merely truncated i e clipped This applies to the leading edge if lt 0 is specified and to the trailing edge if the chord exceeds the width of the diagram If the leading edge locations are not alterred by a preceding line with NUPU 999 the largest chord should be given first if all the other airfoils are to be plotted in their entirety If only the leading edge region is to be plotted to a large scale a normal width is specified for the first airfoil The second airfoil is specified with a very large chord Everything aft of the leading edge region is thus truncated Figure 2 was produced using this option as well If only the trailing edge region is to be plotted to a large scale the first airfoil is specified with 27 lt 0 and a chord c that corresponds to the available paper size s i e c 5 Zie Other regions e g the flap hinge can also be plotted to a large scale First the width of the plot is specified and then the airfoil with large c and e lt 0 such that the desired region falls within the diagram The f
24. values is the span of the aircraft not the half span The chords finally evaluated are t 14 Gao 14 The wing area is S Me 15 where the reference wing area S is S X cab 16 The aircraft mass is W W 4 S S DWS 17 If no alteration of the planform is intended F must be negative which sets t c t c The speed polars computed by PLW lines can also be plotted The scales of the axes are adapted to the results The results from several PLW lines can be plotted in one diagram The labelling options consider two different kinds of comparisons One airfoil with different PLW lines for evaluating different aircraft layouts Different airfoils for evaluating their influence for the same or similar layouts Speed polars which show the sink rate and L D versus aircraft speed and power polars which show the power required in kW versus aircraft speed can be plotted If NUPA 1 2 6 or 7 the arrays containing the polar results are cleared and the results for the current polar are stored for later processing If NUPA 1 or 6 the current polar is plotted in a new diagram the axes are drawn and labelled and the diagram is closed The results for this polar remain available for further plotting If NUPA 3 or 8 the results for the current polar are stored and all the polars stored thus far are plotted the axes are adapted to the maximum and minimum results and the diagram is closed The results remain ava
25. warning x if a drag contribution from laminar separation bubbles is present an information on the sequence of the most significant boundary layer points on both surfaces separated by a slash where it designates beginning instability laminar separation laminar reattachment t laminar turbulent transition R reattachment after separation bubble S turbulent separation A reattachment after turbulent separation wn if mpr 2 9 the listing containing in addition to the summary the boundary layer develop ment along both surfaces for each MU R pair and all the a values in the preceding ALFA line is produced The arc lengths s c starting at the stagnation point the potential flow velocity U Us and the point numbers beginning with zero are given in the first three columns Then for each MU R pair two columns are produced The first one contains H12 for mpr 4 and 8 for all others it contains Hz The second column contains if mpr 2 the momentum thickness given as 10 entitled 100DLT2 if mpr 3 the Reynolds number based on the momentum thickness and the local velocity given as 10 R5 entitled RD2 1000 6 BOUNDARY LAYER ANALYSIS 46 if mpr 4 the displacement thickness given as 10 entitled 100DLT1 if mpr 5 the contribution to the vicous drag resulting from equation 5 using the local H and da entitled CD s if mpr 6 the dif
26. x value of the maximum thickness R h c which is the thickness of the trailing edge in percent chord T t c which is the airfoil thickness in percent chord 4 POTENTIAL FLOW AIRFOIL ANALYSIS 20 A typical EXTRA airfoil with its input are given in Fig 5 EXTRA 12 12 FXPROuuuu9 EXTRA 12610204 5112 Figure 5 EXTRA airfoil having 12 percent chord thickness at z c 0 2 4 1 4 Coordinate Lines Only the options specified by NUPU 0 3 require succeeding lines containing coordinates Wort mann airfoils i e NUPU 0 or 1 are specified by pairs of ordinates y c us and y c is for which x c values are computed by the code The airfoils defined by arbitrary coordinates i e NUPU 2 are specified by one pair of coordinates x and y for each point The thickness distributions of NACA 6 series airfoils i e NUPU 3 are specified in the same way Thus pairs of numbers are specified in the input lines which are read in the same way for all four options The coordinate lines contain one pair of numbers per line The numbers must be separated by at least one space The format of the first coordinate line is used to read all the succeeding coordinate lines The various options require different pairs as follows If NUPU 0 or 1 i e Wortmann airfoils each pair contains the ordinate y c of the upper surface and the ordinate of the lower surface for one abscissa z c The pairs start at the trailing edge as presented in
27. 00000 0 000000 10 00 0 000007 0 111141 1 168386 1 100000 Airfoil NACA 0009 9 Moments delta 0 deg Hinge at x 0 4 y 0 Alpha relative to the chord 1 ALPHA CM CH CL CL LIN 10 00 0 060703 0 060703 1 168387 1 100000 0 00 0 000000 0 000000 0 000000 0 000000 10 00 0 060702 0 060702 1 168386 1 100000 PANEL METHOD NACA 0009 9 CL 0 363964 6 742775 ALPHAO 3 089734 MACH 0 Airfoil NACA 0009 9 Moments delta 5 deg Hinge at x 0 75 y 0 Alpha relative to the chord l ALPHA CM CH CL CL LIN 10 00 0 011974 0 000741 0 808646 0 760129 0 00 0 049861 0 004984 0 363829 0 339871 10 00 0 108545 0 010336 1 524523 1 439871 Airfoil NACA 0009 9 Moments delta 5 deg Hinge at x 0 75 y 0 Alpha relative to the chord l ALPHA CM CH CL CL LIN 10 00 0 000741 0 000741 0 808646 0 760129 0 00 0 004984 0 004984 0 363829 0 339871 10 00 0 010336 0 010336 1 524523 1 439871 PANEL METHOD NACA 0009 9 Airfoil NACA 0009 9 CL 0 783348 6 719803 ALPHAO 6 649134 MACH 0 Moments delta 10 deg Hinge at x 0 9192 y 0 014887 Alpha relative to the chord l ALPHA CM CH CL CL LIN 10 00 0 014017 0 000858 0 391355 0 368595 0 00 0 019818 0 001147 0 781171 0 731405 10 00 0 024346 0 001359 1 928365 1 831405 32 CL 0 000000486 6 74718 ALPHAO 0 000004127 MACH 0 Six blocks of results are produced Each contains a table with a Cm Ch Co and cp lin where ce is computed from the potential flow i e inviscid velocity
28. 05 06 x 07 W 4 w 0 9 0 9 0 8 0 8 OT 1215 0 05 p 0 25 OT 1215 0 05 p 0 25 gt Ramp Avy 4 Av 2 gt Ramp Av 4 Av 15 0 6 T T T 0 6 T T T 02 03 OF 05 06 x 07 02 03 OF 05 06 x 07 W 4 w 0 9 0 9 0 8 0 8 07 1215 0 05 p 0 25 07 1215 0 05 p 0 25 gt Ramp Av 4 Av 1 gt Ramp Av 4 Av 0 3 0 6 T T T 0 6 T T T 02 03 OF 05 06 x 07 02 03 OF 05 06 x 07 Figure 3 Effect of input variation on ramps 3 AIRFOIL DESIGN 13 The following input yields the airfoil shown in figure 4 TRA 77 O 10 60 5 RAMP 4233 TRA2 77 4 145 2 1 7 4 12 521 76 30 ALFA 25 10 DIAG 1 08 12 1412 21 oc relative to the zero lift line Figure 4 Airfoil with ramps on upper and lower surfaces 3 4 ABSZ Line Four values can be changed by the ABSZ line the print mode mpr for the design iteration the number of lines per page in the listing the number of points NQ in the design method and a precision e in the panel method If NUPA 4H 0 mpr NUPE where mpr 0 suppresses the listing from the solution of the transcendental equation mpr 1 produces the default listing as described in the preceding section and mpr gt 2 produces a listing for every iteration NUPI and NUPU are ignored If F 0 the number of lines per page NPG F the default value is 68 If Fy 0 ABFA Fy the default value is 1 If F3 0 EPSPA 0 001F3 the default value
29. 12 00 60 0000 2 00 1 182 0 641 0 622 1 000 0 056868 14 50 4 00 THICKNESS 18 84 CMO 0 1232 ALFAO 4 8721 DEG ETA 1 1364 Airfoils having sharp or thin leading edges are usually not defined precisely enough in that region by the number of points specified in the TRA1 line even if the maximum number is specified Moreover another problem arises even if the airfoil shape is well defined The point on the airfoil that corresponds to the aerodynamic leading edge v usually does not coincide with one of the computed airfoil points Thus for high or low lift coefficients the leading edge suction peak occurs at a location that is not an airfoil coordinate Because the velocities for all the plots and the boundary layer computations are computed only at the airfoil coordinates the resulting suction peak is therefore usually lower than it should be and the boundary layer development is computed with a shallower adverse pressure gradient near the leading edge The low drag range is then predicted to be slightly too wide This small error is unconservative and compounds an error in the same direction arising from the integral method used for the boundary layer computation Accordingly additional points are automatically inserted near the leading edge the code determines how many additional points are required the sharper the leading edge the more points added The points are added in the circle plane at Vir Av where Av 0 5 0
30. 53 2284 4114 FX63 13713 4711 2631 5323 2729 5962 2768 6605 2745 7273 2668 7927 FX63 13719 8590 2343 9204 2098 9804 181310331 147510823 111211221 FX63 1372511578 30711833 10312042 48612137 84812191 116712128 FX63 1373112024 168811792 189511522 203411122 216110704 222010165 FX63 13737 9622 2263 8975 2256 8323 2180 7611 2122 6864 1978 6089 FX63 13743 5304 1699 4480 1482 3625 1254 2740 995 1820 636 985 FX63 13749 000 000 ALFA 148 12 DIAG 1 FXPR 30 FROM THE NEW BOOK FX 63 137 FX63 13701 000 000 82 40 249 169 501 373 818 630 1189 FX63 137 7 1601 1219 2043 1514 2516 1794 3018 2052 3553 2284 4114 FX63 13713 4711 2631 5323 2729 5962 2768 6605 2745 7273 2668 7927 FX63 13719 8590 2343 9204 2098 9804 181310331 147510823 111211221 FX63 1372511578 30711833 10312042 48612137 84812191 116712128 FX63 1373112024 168811792 189511522 203411122 216110704 222010165 FX63 13737 9622 2263 8975 2256 8323 2180 7611 2122 6864 1978 6089 FX63 13743 5304 1699 4480 1482 3625 1254 2740 995 1820 636 985 FX63 13749 000 000 ALFA 148 12 DIAG 2 1 2 1 2 1933 422 16 43 25 1 5 7 PUXY Line 921 2479 2530 716 1460 2277 1855 317 921 2479 2530 716 1460 2277 1855 317 40 The PUXY line writes the airfoil coordinates x c and y c and the inner normal angles 8 to a file having the name of the input file and the extension PU 6 BOUNDARY LAYER ANALYSIS 41 EPPLER 2000 V 13 4 00 29 1 01 20 52 Figure 16 Velocity di
31. A SB homed GED Boe A eee ay a eR des BG 222 WREMOCLING soo te elas te oi yee ot wee gene Gite BTR ge eee te A 225 ENDE ES a oie ik oie as ea ease Yaria Se ee Be eee et 3 Airfoil Design 3 1 3 2 3 3 3 4 4 1 4 2 PRAT inezi ee ren ana a DE ts oa RAZINE a ett a heehee Se Ace ante n Roth hy das E RAMP Liner ars G8 Ga Slo Gee fie ee E SOS S256 Soh SS ABSZ Kine Feo BM eee Di A ear eg eae Bie a Potential Flow Airfoil Analysis FXPR LiNE i i oe Moti E OS ei ee ei ee ee BEER ERED 4 1 1 Coordinate Smoothing Gis ent Ds EA e gf aS 4 1 2 Insertion of Additional Points 200 962 sea e ew ee Gos 4 1 3 Input of Coordinates coke ee ok ees hake de ah ee ee koe HS 4 1 4 Coordinate Lines due 6 408 ieee a Seek a Shite Me e Aid BSE A PAN snes a Gat AS lee ee eee Gee 4 2 1 Switching from Design to Analysis Mode 0 422 Cascades IA AE O 5 Options for Both Design and Analysis Modes 5 1 5 2 5 3 5 4 5 5 SPR LINE S 22 oo 20 Berd E R DY STERK Linea ee ott A ate a ab oh gts tc A ok bd ht ele 2 ue oe hd MACH Eine ia pad an pie Bie gy ten Boe et tas owe ot Sane eG ae PAR Tine Gi aie ee bs a Gta eine he ete a ee Se ee ee a KAT Simple Plas ee a he a ee ee Pee Ree BAe he 5 4 2 Variable Geometry 4 8 44 6 bie aha 6 Ee ae 4s bod Wah ded Qn ded 5 4 3 Modification of Individual Points 2 202004 5 4 4 Moment Reference Points 0 000 eee ee ee ACFA Liness a A oh Soo
32. AG 1 PAN 9 5 7 15 PAN ALFA DIAG 2 1 0511 622 0512 22 1C0 2C x3C 4C REMO1 P PAN 9 6 5 3 90 ENDE 1 5 44 2 152 332 44 Test Cascade Option ac relative to the zero lift line 0 5 SH8 14 86 0 0 5 x c 1 Figure 7 Velocity distributions for SH8 airfoil alone and in a cascade having 15 members denoted by c 5 Options for Both Design and Analysis Modes After defining an airfoil in either the design or analysis mode several options are available for additional printed and plotted output All the options are independent of the mode design or analysis in which the airfoil was defined 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 23 5 1 STRD Line The STRD line prepares the data for plotting airfoils having various chords NUPA is ignored NUPE and NUPI together form the number nn 10NUPE NUPI which is the number of the output file containing an augmented set of coordinates see STRK Line Chap 5 2 The default value of nn is 0 NUPU is the plot mode mzz for subsequent plotting initiated by STRK lines If NUPU 4 0 mzz NUPU If mzz gt 0 the x axis is plotted If maz lt 0 the x axis is not plotted If NUPU 0 mzz remains as previously set The default value is 0 100F Y BL where Y BL is the height of the diagram in mm The sign of Y BL determines the interpretation of F gt 100F RUA where if YBL lt 0 RUA is the vertical distance in mm between th
33. AIRFOIL PROGRAM SYSTEM PROFILO5 USER S GUIDE by Richard Eppler Prof Dr Richard Eppler August 2006 Preface The airfoil program system has been developed over a period of almost 50 years A significant mile stone was the description of the code in cooperation with NASA Langley Research Center in 1980 ref 1 Shortly thereafter a supplement to this description was published ref 2 which included the options for boundary layer displacement iteration and single roughness elements Since then many additional options have been incorporated as described in additional supplements Moreover the book describing airfoil design using the code ref 3 represents another milestone The version of the code listed in reference 1 is sold in the U S without my consent The same version was available from NASA through the Computer Software Management Information Center at the University of Georgia This version is obsolete Two major improvements were incorporated in 1996 First a new transition criterion was developed that considers the instability history of the boundary layer the previous criterion was local Second an empirical model for the drag due to laminar separation bubbles was included the previous version provided only warnings of bubbles and no estimate of the drag Over the past decade additional theoretical and experimental results concerning transition and lam inar separation bubbles and much faster comp
34. LFF sentence containing NQ A R and T The airfoil name is always read and written in the listing the numbers NQ A R and T are not always used If one of the DLFF words is specified all preceding words must be given even if they are not used The words following the last specified word may be omitted If NUPU gt 4 the FXPR line and the succeeding line contain everything necessary to compute the corresponding coordinates If NUPU lt 3 additional information specified in subsequent lines is required Wortmann Airfoils If NUPU 0 or 1 optionally 10S where S lt 10 Wortmann FX airfoils are specified NQ R and T are ignored A specifies a modification factor TH F Only the ordinates i e y c must be given in the succeeding lines beginning at the trailing edge as presented in reference 7 The abscissas i e z c are computed in Subroutine FIXLES The various formats of the succeeding lines containing the ordinates are described in the Chapter 4 1 4 In reference 7 two sizes of coordinate sets are presented one with 49 points on each surface the other with 44 In the latter case several points near the trailing edge have been omitted Accordingly the code counts the number of input points and then computes the corresponding z c values In the former case the airfoil is defined by 97 points in the latter by 87 The leading edge point is included on both surfaces in reference 7 whereas only one point is req
35. MO line at least two spaces after the last number these two letters replace YY in the table 9 followed by two letters accom plishes the same for ZZ The replacement letters precede the airfoil number if NUPA 8 or 9 with a space if NUPA 8 and without a space if NUPA 9 E O OND OO BW NY TL MH DO YY ZZ E S HQ HX NUPE NUPI and NUPU are ignored and therefore columns 7 10 can be used for the airfoil iden tification number if desired Fi specifies A which is the beginning of the closure contribution on the upper surface F specifies A which is the beginning of the main pressure recovery region on the upper surface F specifies RSM us which is the recovery specification mode for the upper surface It determines the interpretation of F4 and F as shown in the table to the right Fe specifies N is the beginning of the closure contribution on the lower surface F specifies A N A is the beginning of the main pressure recovery region on the lower surface Fx specifies RSM Is which is the recovery specification mode for the lower surface It determines the interpretation of Fy and Fig as shown in the tableto the right 0 1 2 3 K Ww H H L w w ww The values of K u K and ji are normally rounded to three digits after the decimal point the values of a to two digits F numbers F3 and Fg allow the rounding to be changed If the first d
36. ae a SS SO SSS Sw oda ana 11 13 14 14 15 16 17 20 20 20 21 CONTENTS 5 6 DIAG Line 5 6 1 PressuresEnvelope Diagram 2 44 4 246 4 Seeg y aee eed A A RN 5 7 PUXY Line 6 Boundary Layer Analysis 0 17 IBUNGAMENEAISS fz Sete a ete ltda E eck Ho Ee ee ao ee eee 6 1 1 Criteria for Boundary Layer Transition 2 05 6 14 Profile Dias otha A Be ee ee oes 613 Bubble Diag iano ao a is a gee eee eae A 62 ERIN Ne 5 2 os 2 nl 8 a kl eth Baal oh a A ee Ue y 0 3 RE Eine soja oe te e WOR ee le ele dl a BSS me RA al a 6 3 1 _ Print and Plot M d s o ccc soc ee as ia Gn eee el e E 6 3 2 Reynolds Numbers and Transition and Bubble Drag Modes 6 3 3 Single Roughness Elements 0 e 6 34 Labelling and Scaling CA E A ee em a ea ed 6 3 5 Interpolation of Drag and Lift Coefficients OAs FEZW Eese 2 e ind Sach a ti ec Sec A lee ee Seance ad Gane ed den do Be 2 ob EL EIS E ee a re SR RO a 6 0 RLWA ENE e saca o rr Sete Reid he tee into oh eRe A Ach ee Bee der Je 0 CDCl dines a e o s Su EA fd eee E SOE PESOS SS 3 6 7 1 Extension of Frame cia EA ea ee ee ee ee oe ee 02 habe ling vt a A O A O e Ae wae ale eee deg amp 6 7 3 Experimental Data ue o ote Be he Be ad aire Wil da ee Ould Emne Types cadens Bis ese ss le Bs tS bi Be ee Se eee 69 A A ATTE A NENE 0 0 Empty Grida canti ao ds te e bt e e da be ol Oillo Examples 2 GAN E rs TA a a A 6 8 MIRTA id e a de 7 Rules fo
37. am remains open for further plotting if mpl 7 the curves for the first MU R pair are plotted into the open diagram which is then closed and if mpl 8 the curves for the first MU R pair are plotted into the open diagram which remains open for further plotting If NUPA 0 mpr and mpl remain as previously set The default values are mpr 1 and mpl 0 If 0 lt NUPU lt 99 the amplification diagrams as shown in figure 17 are plotted for all boundary layer computations initiated by this RE Line Thus the number of figures is 2 times the number of angles of attack times the number of MU R pairs i e one figure for each surface at each a for each MU R pair The number of figures is limited to NUPU if NUPU lt 99 and to 999 if NUPU 99 6 3 2 Reynolds Numbers and Transition and Bubble Drag Modes If NUPA 4 9 and NUPU 0 the boundary layer computation is performed F numbers Fi Fio are interpreted as follows F MU which contains five digits sa bcd which are interpreted as described below F gt 10R where R is the Reynolds number If F 0 the MU R pairs and the values of x7 c from the preceding RE line are used 6 BOUNDARY LAYER ANALYSIS 47 F3 F4 MU2 Ra and so on up to Fo Fio MUs Rs F numbers F F 9 specify single roughness elements see Chap 6 3 3 The odd F numbers F1 F3 Fy each contain five digits sa 0c which are interpreted as follows s is the suction mode MA which is
38. ape is modified to simulate the deflection of a simple flap NUPA must be zero F specifies the length of the flap in percent chord F specifies the vertical location of the flap hinge in percent chord Thus the flap hinge point is located at z c 1 0 01F and y c 0 01F 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 28 F specifies one half the transition arc length s7 c in percent chord for the upper surface Typically sy c 0 04 0 06 depending on the amount of flap deflection F specifies the flap deflection 0 in degrees positive downward F specifies one half the transition arc length s7 c in percent chord for the lower surface If F 0 or blank the transition arc length for the upper surface is also used for the lower surface For example FLAP i252 43 10 which specifies a simple 25 percent chord flap with a downward deflection of 10 The flap hinge is located vertically at y c 0 02 and the transition arc length is s7 c 0 06 for the upper surface as well as for the lower surface 5 4 2 Variable Geometry If NUPU 1 5 the variable geometry option is specified The points are renumbered during the execution of each of the following FLAP lines If NUPU 1 points are deleted The digits of the F numbers are denoted F aaa bb Points aaa to aaa bb are deleted If bb 00 only point aaa is deleted The points after point aaa are renumbered If it is intended that aaa i always be the point nu
39. area in kg m F gt Vmax Which is the maximum aircraft speed in m s 0 1 F3 p which is the air density in kg m If F 0 p remains as previously set The default value is 1 229 kg m F 10 v which is the kinematic viscosity in m s If F 0 y remains as previously set The default value is 13 6 x 10 m s F c which ts the local chord in m If F 0 the FLZW line does not initiate a boundary layer computation instead the values of Umax P and y are stored for a succeeding PLW line Fg smmmb cc where s may be a minus sign sb cc is the local twist angle in degrees and mmm is the transition mode for the chord specified by F5 This option is only permitted if NUPU in the FLZW line is zero If not m is included in the twist angle which can then be greater than 10 If NUPU 0 and the twist angle is less than 10 the transition mode is taken from the first transition mode in the preceding RE line If mmm 0 it is set to 300 Fz Fs c2 O2 and so on up to Fis Fis c5 O5 6 5 PLW Line The PLW line initiates an aircraft oriented boundary layer computation using the specified aircraft data and resulting in a speed or a power polar for the given aircraft The wing planform is specified and therefore the aspect ratio can be computed and the influence of the local chords on the 6 BOUNDARY LAYER ANALYSIS 51 Reynolds number can be considered Knowing AR allows the induced drag coefficient C p
40. ary of the options follows the details are given in Chapter 4 1 3 If N 0 or 1 the ordinates i e y c of a Wortmann airfoil are read the abscissas i e x c are computed If N 2 arbitrary coordinates x c and y c are read If N 3 the upper surface coordinates of a symmetric NACA 6 series airfoil i e thickness distribution are read the mean line and the coordinates of a cambered NACA 6 series airfoil are then computed If N 4 the coordinates of an NACA 4 digit series airfoil are computed If N 5 the coordinates of an NACA 5 digit series airfoil are computed If N 7 a curve of the form Ym ax c a ba c 2 is computed and the x axis of a previously given airfoil is transformed into this curve which yields additional camber If N 8 the x axis of a previously given airfoil is transformed into a circular arc If N 9 the coordinates of a symmetric EXTRA airfoil consisting of an ellipse and two straight lines are computed The F numbers F specify additional points to be splined in see Chap 4 1 2 4 1 1 Coordinate Smoothing The second digit S of NUPU in an FXPR line allows the coordinates read from the subsequent lines to be modified to eliminate irregularities Wortmann and some other older airfoils require such smoothing Two options are available If S gt 1 and N 1 a mild smoothing is performed S times S 3 is sufficient for most airfoils This option applies only to Wortmann
41. ary to several other lines e g ALFA RE FLZW and PLW the input from which remains in effect until replaced by that from a new line of the same type the MACH line remains in effect only until a new airfoil is defined by TRA1 and TRA2 lines or by an FXPR line and the corresponding coordinate lines After either of these line sequences the Mach number is reset to 0 and another MACH line is required if the new airfoil is to be computed with M 0 It is not necessary to insert the MACH line immediately after the definition of an airfoil Thus it is possible to evaluate the differences between the incompressible and compressible flows The following example fig 9 plots a diagram containing two velocity distributions for one airfoil the first is incompressible the second compressible with M 0 55 Note that some of the labels are not specified by the example input The diagram includes the sonic limit if it is near the maximum velocity on the airfoil The Mach number M and the value Mc for the last a are also plotted The compressibility correction is invalid if the sonic limit is exceeded TRA1 TRA2 lines ALFA 238 MACH TEST 8 3 93 DIAG 1 ae a ai IA Da ALFA 7 DIAG 2 ac relative to the zero lift line 0 5 SH9 15 86 0 0 5 x c 1 Figure 9 Velocity distributions for SH9 airfoil at M 0 and M 0 55 identified by c 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 27 5 4 FLAP Line The FLAP li
42. ch different sets of data can be plotted in one diagram V s near the leading edge can be plotted and the airfoil points can be identified by symbols The three digits of NUPU are designated abc If c 0 one set of data is plotted axes are drawn and the diagram is terminated i e closed to further plotting If c 1 one set of data is plotted and the diagram remains open to further plotting If c 2 one set of data is plotted into the open diagram axes are drawn and the diagram is terminated If c 3 one set of data is plotted into the open diagram which remains open to further plotting If b 0 the airfoil points are identified by symbol b as defined in figure 12 In this case only the first eight symbols are available symbol 9 is a flag perpendicular to the airfoil surface If a 0 V s near the leading edge is plotted The velocities on the lower surface are plotted as negative values Obviously plot mode mbt is valid only for the one DIAG line in which it is specified 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 36 x Avyr BOA YT POOoOxX da EBOAY A 1 2 3 amp 5 6 7 8 9 10 N 12 13 14 15 16 17 18 19 20 Figure 12 Available symbols and their numbers Symbol 10 is a flag perpendicular to the local tangent 5 6 1 Pressure Envelope Diagram If NUPI 1 a pressure envelope diagram is plotted The abscissa is C min and the ordinate a All a values in the preceding ALFA line are used The size of th
43. ckness and if present the turbulator locations are plotted Below this the line types and their corresponding explanations are plotted in a key Normally these explanations contain the Reynolds numbers from the RE line or the chords from the FLZW line that precedes the CDCL line that terminates the diagram i e NUPU 0 2 or 4 For each Reynolds number or chord the line type is drawn followed by the Reynolds number or chord and the roughness factor r if it is not zero The explanation is supplemented by without b d if the bubble drag contribution is not included in the plotted c values with b d u or with b d is added if the bubble drag is included for only the upper or lower surface respectively Labels can be placed near the transition and separation curves for the upper and lower surfaces as well as near the ce and Cm curves The input for this option begins at least three columns after the last F number or in column 13 or higher if no F numbers are specified One or more DLFF sentences can be given which contain up to 14 groups of three DLFF words as follows k c ze k c te These groups determine the positions of the six labels T U T L S U S L co a and Cm a in that order The abbreviations stand for transition upper surface transition lower surface separation upper surface and separation lower surface respectively The groups of
44. computations Depending on the print mode mcm the coefficients can be listed immediately after they are computed A FLAP line with NUPU 0 automatically shifts the reference point for c to the flap hinge point The computation of cp is performed such that only that portion of the airfoil aft of the reference point contributes to ca The hinge moment coefficient c is nondimensionalized by the airfoil chord not by the flap chord This works properly only if the coordinates are not normalized by a FXPR or PAN line with NUPI 0 Occasionally moments relative to other reference points must be computed which can be accom plished by means of a FLAP line with NUPI 0 NUPA NUPE and NUPU are ignored If NUPI 1 the reference point for both c and c is shifted to z c COL y c 0 01F gt If NUPI 2 the reference point for both cm and cp is shifted to the point specified by F and F as with NUPI 1 but the calculation of m excludes that portion of the airfoil forward of the reference point If NUPI gt 3 the F numbers are ignored and the reference point for c is the flap hinge point The calculation of cm is performed as with NUPI 2 This FLAP line immediately initiates the computation of Cm and c about the new reference point for all values in the currently valid ALFA line Depending on the print mode specified in this ALFA line a listing of the moment coefficients is produced in which the reference point is given The o
45. covery function and the horizontal line w 1 lies forward of the beginning of the ramp In this case the code writes a message and ignores the ramp design In such cases either Av must be increased or Av must be decreased The length of the ramp is constrained only by the length of the given airfoil surface It is permitted to change a within the ramp as can also be done within the recovery function It is recommended however that only one a be specified for both the recovery function and the ramp NUPA NUPE NUPI and NUPU are ignored F Avy for the upper surface F Av for the upper surface F Avy for the lower surface and F Av for the lower surface The RAMP line is valid for the current airfoil design only and must be inserted ahead of the TRA2 line At the end of Subroutine TRAPRO which computes the airfoil coordinates the values of Av and Av are reset to the default values i e zero which specify no ramp The option of specifying 2 instead of a in the TRA1 line Chap 3 1 is independent of the RAMP line 3 AIRFOIL DESIGN 12 087 4215 0 05 pal 087 4215 0 05 pal Ramp Av 4 Avr 2 Ramp Av 4 Av 1 5 0 7 T T T 0 7 T T T 02 03 OF 05 06 x 07 02 03 OF 05 06 x 07 087 125 0 05 pal Oe IES 20 5 eI gt Ramp Avy 4 Av 1 gt Ramp Avy 4 Av 0 5 0 7 T T T 0 7 T T T 02 03 OF 05 06 x 07 02 03 OF
46. d although the value of N must be determined empirically The amplification is only a factor by which very small initial disturbancies are amplified The amplitude of the TS waves at the beginning of the transition process has been extensively investigated Mea surements in low turbulence wind tunnels correspond to an N of 11 to 13 Measurements in flight correspond to N values up to 15 Note that the N values of 11 13 and 15 represent amplifications of 59 874 442 413 and 3 269 017 respectively The default value of N in the code is 11 which corresponds to a low turbulence wind tunnel but may be conservative for flight The value of N can be specified in the input For previous transition criteria a roughness factor r gt 0 could be specified that accounts for free stream turbulence and or surface roughness For the eN method the roughness factor specifies a reduced N factor N as follows N N 1 0 1657 Thus an r of 6 specifies an N factor N of 0 01N which means transition will occur immediately after the initial instability This simulates a very rough surface and or a very turbulent free stream A roughness factor r of 0 corresponds to natural transition on a smooth surface with very low free stream turbulence The effect of single roughness elements has also been included which simulates turbulators flap hinges or poorly faired spoilers for example If the boundary layer is turbulent at the location of the roughness ele
47. d nAA to Ap where n 1 N MOD and lists the resulting polars Thus if NMOD 3 three polars are generated If only one parameter is to be changed the other changes must be set to 0 NUPA NUPE and NUPI perform the same functions as in the PLW line although some restrictions apply The PLWA line produces more than one polar if NUPU gt 1 Such a PLWA line specifies the one value of NUPA that will be used for all the polars If NUPU gt 1 only NUPA 4 or 9 makes sense with respect to the sequence of the plots Moreover all the polars resulting from NUPU gt 1 are plotted with the one symbol specified by NUPE in this line It is thus not possible to have different symbols for the curves of the different polars and only one explanation option can be used Therefore it is recommended that the plotting option in the PLWA line be exercised only with NUPU 1 which means that only one modification of the aircraft parameters is initiated by each PLWA line There may be more than one PLWA line after a PLW line of course and each may exercise the plot option in exactly the same way as the PLW line with no restrictions on the NUPA and NUPE values 6 BOUNDARY LAYER ANALYSIS 55 6 7 CDCL Line The CDCL line plots the boundary layer summary i e section characteristics which contains the lift drag and pitching moment coefficients including viscous corrections In addition the transition and separation locations are shown The abscissa
48. data fig 23 CDCL 9 3 0 O 1 2 1 011 8 13 16 01 NExonly 100 12 23 34 45 56 67 78 89 100 105 10000 123 98 94 104 112 119 125 134 160 240 F TO1Special Experiment 100 90 86 82 78 74 70 65 60 50 10 6 10 80 67 54 41 30 19 8 3 40 90 6 10 70 60 50 40 20 0 5 6 10 30 100 5 5 6 6 6 7 7 7 8 4 6 A 100 10 50 70 80 85 90 95 99 100 100 6 HSC ePHOUOr 6 BOUNDARY LAYER ANALYSIS 65 Test Exp Data SH8 14 86 R 2 0x10 y 6 0x10 see y 1 5 Exp Re 2x10 ao Y x Exp Re 6x10 _5 Co y 1 v 05 L Doa 0 T I T T T T T Y T i T 0 5 10 15 10 20 Figure 22 Diagram for two Reynolds numbers including experimental data EPPLER 2000 V 13 4 00 25 1 01 11 46 _ Cy Exonly 16 01 74a a Special Experiment a a E i ee Lee pE O c 7 ee or 2 Ed Gf L y d 2 Q45 0 5 a of 0 5 K lee A 8 op EN PO A A 4 o oO o O 10 9 gt x 10 p 0 ae ty 10 15 20 10 25 b 0 5 x 1 Figure 23 Diagram containing only experimental data 6 8 DPIT Line The DPIT line initiates a boundary layer displacement iteration Because the iteration process can diverge the DPIT line should normally specify only one iteration A maximum of five angles of attack from the currently valid ALFA line can be specified for the displacement iteration The succeeding RE or FLZW or PLW line initiates the normal boundary layer computat
49. data can be included in the diagram as follows If NUPE 0 8 and NUPU 0 1 4 or 5 i e a CDCL line that opens the diagram the frame dimensions and the airfoil name are determined by the results to be plotted by this line including the experimental data if NUPE 0 see below If NUPE 9 NUPU is ignored and the frame dimensions and the airfoil name must be specified in the CDCL line The values of Cemar and Comin are given in Fy and Fs respectively as previously discussed The airfoil name is specified after N as in other lines F3 Ce maz Which determines the upper edge of the frame as previously discussed F5 Ce min Which determines the lower edge of the frame as previously discussed Fe Camin Which shifts the cg axis as is normally performed automatically if Camin gt 0 01 The default value is 0 6 BOUNDARY LAYER ANALYSIS 59 F7 Qmin Which determines the left end ajc of the a axis as follows eft MAL Amin 4 10 Fg Omar Which determines the right end a ign of the a axis as follows Qright M N Amar 3 19 Fg t c which is the airfoil thickness in percent chord If this value is not specified the thickness is not plotted after the airfoil name Fio Cm min Which is the minimum pitching moment coefficient The default value is 0 1 Fii Cm max Which is the maximum pitching moment coefficient The default value is 0 The experimental results are specified in additional l
50. dicates those portions of the boundary layer development that contribute most to the drag See ref 3 6 1 3 Bubble Drag At low Reynolds numbers the occurrence of laminar separation bubbles is the reason for most and sometimes large differences between wind tunnel measurements and numerical predictions based on boundary layer theory The boundary layer method in the previous versions of the code used an analogy between the turbulent boundary layer just after transition and the laminar separation bubble This analogy has been used since 1982 to issue a warning when additional drag from bubbles was to be expected Since 1996 a technique for estimating the bubble drag was derived from recent experimental results This model however had a shortcoming that was present in most other simulations as well Near the leading edge where laminar separation occurs in a very thin boundary layer the predicted bubble drag was too high This has been corrected Theoretical investigations showed that following separation a thin laminar boundary layer exhibits a considerably adverse pressure gradient Accounting for this pressure gradient led to much better agreement with experiments for thin and thick boundary layers Another finding from the theoretical investigations was the existence of an explosively increasing dissipation coefficient near transition in the separated boundary layer This has been confirmed experimentally Introducing this phenomenon into t
51. distribution and cg lin includes viscous effects merely by setting the lift curve slope to 27 or 0 11 per degree The first block contains cm about the quarter chord point and c about the leading edge Because no portion of the airfoil is forward of the reference point for cy i e the leading edge c is identical 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 33 to the moment coefficient about the leading edge The second block contains cm about z c 0 2605 y c 0 which is the aerodynamic center The hinge moment coefficient cp is still computed about the leading edge The third block contains cm and c about z c 0 4 y c 0 which is a hinge point The contri bution of the portion of the airfoil forward of the hinge point is excluded The fourth block which concerns a 25 percent chord flap deflected 5 contains c about the pre vious hinge point z c 0 4 y c 0 and c about z c 0 75 y c 0 which is the hinge point introduced by a preceding FLAP line The fifth block contains cm and c about z c 0 75 y c 0 The sixth block which concerns an additional 8 percent chord flap deflected 10 contains c about z c 0 75 y c 0 and c about the new hinge point z c 0 9192 y c 0 0149 5 5 ALFA Line The ALFA line initiates the storage of up to 22 angles of attack specified by the F numbers all values remain available for other options the inviscid computation of the pitching moment and hi
52. e specified c is less than the minimum or greater than the maximum value of ce or respectively along the corresponding curve Occasionally the cy value where the corner e is to be positioned occurs more than once along the curve for example if ce decreases beyond stall In this case the first occurrence of the cy value in the sequence of the currently valid ALFA line is selected The second occurrence can be selected 6 BOUNDARY LAYER ANALYSIS 58 by increasing k by 5 Thus k 7 specifies the second occurrence of the c value c along the curve specified by k 2 If k is negative the label rectangle position is independent of the curve In this case e specifies the horizontal coordinate x c of the upper left corner of the label rectangle and c the cy value After the group of numbers that inserts the last label c 0 up to six more DLFF words W W 5 can be given Wz and W contain the horizontal and vertical positions respectively of the upper left corner of additional text given after E which can be given at least three columns after the last DLFF word The horizontal position is given in the units of the c axis i e between 0 and 35 the vertical position in the units of the c axis An example of this option is given in figure 19 where 1935 is plotted at 12 0 5 W i 2WzL s specify a position of the explanation blocks different from the default position For example if high cy values occur the e
53. e cascade members are treated exactly by the higher order method used for the single airfoil If the cascade has narrow gaps between the members the higher order method is necessary to provide adequate precision Because it is not possible to have an infinite number of members and a higher order panel method the number of members must be specified If the number of cascade members ne is 15 a good approximation to an infinite cascade results An odd number of cascade members is recommended because the airfoil under consideration is then in the middle of the cascade The convergence of the method can be checked by comparing two solutions for the cascade having the same airfoil but different numbers of members The most sensitive result is the second value of ce in the listing from Subroutine PANEL This cy value for 90 is equal to the lift curve slope of the airfoil according to potential flow theory 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 22 The cascade parameters remain unchanged until a new PAN line with NUPA 9 is read The following input generates figure 6 as well as the velocity distributions for the SH8 airfoil at an angle of attack of 9 relative to the zero lift line shown in figure 7 The number of cascade members Ne is 15 and the distance between the members is Ax c 0 5 and Ay c 1 0 REMO1 P RTEST 1CASCADE 10PTION FIGS 6 5 TRA1 8 27 5 10 29 5 11 0 12 60 4 TRA26 8417 5 2 1 7 4 17 5 2 1 7600 ALFA 24 DI
54. e chord line of one airfoil and that of the next and if Y BL gt 0 RUA is the vertical distance in mm between the upper surface of one airfoil and the lower surface of the next F SILAFA which is a scale factor for the label inserted above the leading edge of each airfoil The label contains the name of the airfoil and the thickness The label height is SILAFA times the airfoil chord The airfoil name can be specified as in other diagrams The default value of SILAF A is 0 008 which is suitable for chords greater than 400 mm The value of SILAF A remains in effect until a new value is specified If SILAFA lt 0 no label is plotted F specifies the line width The default value is the value PENLTI which can be specified in the REMO line Chap 2 2 2 The default value of PENLT is 0 4 mm 5 2 STRK Line The STRK line initiates a diagram and a listing of the airfoil coordinates generated by the preceding TRA1 and TRA2 lines or FXPR line for various chords An STRK line must be preceded by an STRD line If NUPA 0 an augmented set of coordinates for each chord is listed Each airfoil diagram increases nn by 1 and then opens a new file LASnn NCC Such files can be used for numerically controlled milling machines for example The coordinates are spaced such that the straight line from one point to the next deviates from the spline fit through the points by less than a constant times 2NUPA Thus the number of coordinates listed increas
55. e frame depends on the a values If the vertical extent of the frame must be increased to accommodate a succeeding set of data this can be accomplished by setting F and F gt 0 If Fy 0 Fi Amin in degrees If F 0 Fy Amaz in degrees 5 6 2 x y V Diagram If NUPI 1 the x y V diagram is plotted If NUPI 0 the curves in the x y V diagram are solid If NUPI gt 2 NUPI is the line type as defined in Chap 6 7 4 The x y V diagram contains the airfoil shape and the velocity or pressure distributions for all a values in the preceding ALFA line The ordinate is V if NUPI 0 or 1 in the ALFA line or C if NUPI 2 or 3 Scaling Usually the diagrams are produced by means of a printer in which case it is helpful to specify the size of the diagrams in the input The length of the x c axis in the velocity or pressure distribution is specified by 100F which is the unit length i e c 1 of the x c axis in mm The default value is 200 mm For example DIAG uuuuuu140 which specifies a length of 140 mm for the 2 c axis Note that the x c axis can extend beyond z c 1 for airfoils with flaps or variable geometry Only DIAG lines that open a diagram i e NUPU 0 or 1 can alter the unit length Extension of Frame The size of the frame for the x y V diagram is determined from the data available when the diagram is opened i e NUPU 0 or 1 The data to be plotted from this line including the experimental data if
56. ead The F numbers are counted If less than five MU R pairs are specified and FF is specified the F numbers between the last MU R pair and F must be specified as zero For example REvuuuuuuuu34000 3 2000 0 0 0 0 0 0 60 1 80 1 which specifies roughness elements on the upper surface at z c 0 60 and on the lower surface at x c 0 80 each with a height h c of 0 0010 These elements are also used for the second Reynolds number 6 3 4 Labelling and Scaling The boundary layer development diagram contains Rs in a logarithmic scale versus H3 in a linear scale Two plots are produced one for the upper surface and one for the lower surface Each plot contains one line for each a value in the currently valid ALFA line Each plot contains the stability limit Rs Hin and a vertical line for laminar separation See reference 3 A boundary layer development diagram is initiated by NUPI 1 8 The different modes for opening and closing the diagram are described in Chapter 6 3 1 The diagram can be supplemented by additional text If Z is given after the optional information for curve labelling see below the character string following Z is inserted between the airfoil name and the Reynolds number All the options described in Chapter 5 6 are available If A and two spaces are given following or immediately preceding the Z sequence the explanation blocks are moved above the plots Starting in column 51 groups of three numbe
57. ed In all DIAG lines with NUPI 0 additional input can begin at least three columns after the last F number if no F number is present in column 13 or higher One or more DLFF sentences can be given that contain one or more groups of three numbers as follows i z c e i z c e Each group of three numbers plots the ith value near the corresponding curve The value is plotted such that the corner e of the label rectangle fig 13 is located at x c along the curve If the sign of x c is negative the curve corresponding to the lower surface is labelled if positive the curve for the upper surface is labelled If a minus sign precedes 7 is plotted ahead of the a value The input e 1 at the end of a sentence can be omitted the next sentence must then begin with 2 for the next group The label rectangle encompasses the label and a small gap The e values corresponding to the four corners are shown on the left side of figure 13 The right side of figure 13 shows an example in which corner 4 is located along the curve If labelling information is input the a values are not plotted in the upper right corner ag eee ee EN e 4 as ce e 4 O O Oe one he e 2 e 3 Figure 13 Label rectangles Note that the character F in any DLFF word can be used to continue the input in the next line The airfoil name to be plotted can be changed by inputing N and the new name as a character string at least three columns afte
58. eding FLZW line are used The print and plot modes for the boundary layer computation cannot be changed by an PLW line NUPA NUPE and NUPI specify options for plotting the computed speed polar see below NUPU MU a0c which is transition mode as described for the FLZW line F t c which is the reference airfoil thickness in percent chord If F lt 0 t c t c which is the thickness of the airfoil being evaluated in percent chord If Fi 0 MU t c W DWS Ap and the reference planform remain as previously specified F W which is the aircraft mass in kg F DWS which is the mass penalty factor in kg m see below 1073F Ap which is the parasite drag area in m F cj which is the local chord in m F db which is the length of the spanwise section having chord cj in m Fz Fg c3 dbz and so on up to Fy_i Fw Cy_1 dbn_1 where N lt 14 Fy 41 k factor if k 0 the default value 1 03 is used The wing planform is specified in F5 Fy by spanwise sections having constant chords A linearly tapered wing of 15 m span having a root chord of 1 2 m and a tip chord of 0 6 m could therefore be described by three 5 m sections db 5 having average chords c of 1 1 m 0 9 m and 0 7 m The same planform could be described by five 3 m sections db 3 having average chords c of 6 BOUNDARY LAYER ANALYSIS 52 1 14 m 1 02 m 0 90 m 0 78 m and 0 66 m Note that the sum of all the db
59. er Absauge Grenzschichten Ingenieur Archiv 32 1963 pp 221 245 English translation NASA TM 75328 1978 5 Eppler Richard About Classical Problems of Airfoi Drag Aerospace Science and Technology Vol 7 2003 pp 289 297 6 Eppler R Independent Plotting R Eppler Stuttgart c 2004 7 Althaus Dieter and Wortmann F X Stuttgarter Profilkatalog F Vieweg amp Sohn Braun schweig 1981 8 Abbott Ira H Von Doenhoff Albert E Theory of Wing Sections Dover Publ New York c 1959 9 Jacobs Eastman N Ward Kenneth E and Pinkerton Robert M Characteristics of 78 Related Airfoil Sections from Tests in the Variable Density Wind Tunnel NACA Rep 460 1933 10 Jacobs Eastman N Pinkerton Robert M Tests in the Variable Density Wind Tunnel of Related Airfoils Having the Maximum Camber Unusually Far Forward NACA Rep 537 1935 11 Labrujere Th E Loeve W and Sloof J W An Approximate Method for the Determi nation of the Pressure Distribution on Wings in the Lower Critical Speed Range Transonic Aerodynamics AGARD CP No 35 1968 12 Drela M and Giles M B Viscous Inviscid Analysis of Transonic and Low Reynolds Number Airfoils AIAA Journal vol 25 no xx 1987 pp 1347 1355 13 Dini P and Maughmer M D A Locally Interactive Laminar Separation Bubble Model J Aircr vol 31 no 4 July Aug 1994 pp 802 810 14 McGhee Robert J Walker Betty S and Milla
60. er surface two points are inserted at x c 1 10 and z c 1 20 Two points are splined in between the original trailing edge and the new point at z c 1 10 three points between gfe 1 10 and z c 1 20 On the lower surface the last point of the original airfoil that was not deleted is near z c 0 84 Its number is 51 after the deletion of three points and insertion of two on the upper surface Aft of that point only two points are inserted one at x c 1 00 number 52 or NQ 1 and the other at x c 1 20 number 53 or NQ The distances between these points as well as between the last point on the original airfoil and the first inserted point are larger than those on the upper surface Therefore four and six points respectively are splined in using negative F This procedure does not require knowledge of the absolute point numbers and still functions properly if for example the transformation i e NUPI 1 that produces the vertical tangent at x 0 y 0 is performed by the FXPR line see Chap 4 1 This is actually performed in this example 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES N OO O 4 yee B 3 o 2 o Se 1 gt Paes 9 9 252NG Points to be deleted x Points to be inserted SS O 9900 19 Figure 10 Alteration of airfoil point numbers during exercise of variable geometry option NACA 23015 VG 12 49 O E N 30 Original point numbers before deleting points by FLAP line wi
61. er to use the factor With the factor N 1 experimental value is allowed in the second DLFF sentence The D A and T lines specify abscissas whereas the L and M lines specify ordinates The data remain available until other data are read Thus for example one set of cy values can be used for both cq and a values A third DLFF sentence may be included following the experimental data It contains only one word that specifies the symbol number The symbols are connected by straight lines if the distance be tween the points is sufficient If the number of abscissas and ordinates is not the same the longer set is truncated starting with the last value The truncation applies only to the diagram all the data remain available for further plotting If a symbol number is specified two symbols and a connecting line are plotted in the key The explanation for this line can be specified in the CDCL line as previously explained or following T which must be given at least three columns after the symbol number The continuation option F can be used if necessary The symbols are shown in figure 12 A flag perpendicular to the curve is not available in this case 6 BOUNDARY LAYER ANALYSIS 60 For example Duw10000 48 49 51 60_ 75 Lot Oy 185570941 tio Su TO 1Exp A ut Auu 14041420345 E which plot five data points as cq versus ce using symbol 5 The cy value of 1 1 is not used The explanation for this line is Exp 1 Then si
62. erefore small discrepancies between the previously published coordinates and those generated by the code are possible Transformation Using Third Degree Polynomial Line If NUPU 7 the x axis of a given airfoil is transformed into a third degree polynomial curve of the form Ym az c x bx c zx The boundary conditions are Yml0 Yymlc 0 YO SA Yne R where c chord and T is ignored The original airfoil must have been specified before the FXPR line with NUPU 7 is read Non symmetrical airfoils can also be modified using this option Each point n Yn of the original airfoil is modified as follows First the point ym n on the mean line y a is computed Then the new point is located perpendicular to the tangent of the curve ym x at n The distance to y x is Yn Transformation Using Circular Arc If NUPU 8 the z axis of a given airfoil is transformed into a circular arc The only diffenence between this option and the preceding one is that the new curve y x is now a circular arc through x 0 and x c with a slope at x 0 of A degrees This option is normally only used for cascades EXTRA Airfoils If NUPU 9 a symmetrical EXTRA airfoil is specified These symmetric airfoils for aerobatic aircraft are defined by an ellipse and two straight lines NQ is the total number of points to be computed A a c which is the length of the half axis of the ellipse in percent chord This is also the
63. es with NUPA The value of NUPA is not stored it must always be specified in the STRK line that initiates the diagram If NUPE F 0 the points resulting from the design or analysis mode are identified by symbols The value of NUPE specifies the symbol and is valid for only one plot Only symbols 1 9 see fig 12 can 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 24 be specified because NUPE has only one digit In this case NUPE 9 specifies symbol 10 instead of symbol 9 Figure 2 which shows the additional points near the leading edge was produced using this option with NUPE 9 If NUPI 0 the listing is produced but the diagram is suppressed If NUPI 0 both the listing and the diagram are produced If NUPU 1 999 the F specify up to 22 chords c in mm which are used for both the listing and the diagram if NUPI 0 If F lt 0 any open diagram is terminated before the diagram containing the airfoil having chord c is opened If F gt 0 the airfoil with chord c is plotted in the diagram that is open to further plotting If no diagram is open or if the open diagram does not contain sufficient vertical space a new diagram is opened before the airfoil with chord c is plotted Any airfoil having a chord c lt 1 mm is not plotted Thus the diagram is terminated by 1 mm lt c lt 0 If NUPU 0 the chords from the preceding STRK line are used If NUPU 999 the F are the z c locations x of the leading edges of
64. ess is omitted after the airfoil name as are the default explanations of the line types The second digit b of NUPU initiates the following If NUPU 0 or 4 only one boundary layer summary is plotted the axes are drawn and labelled and the diagram is closed The frame is adapted to this summary no further input is necessary If NUPU 1 or 5 the diagram is opened one summary is plotted and the diagram remains open to further plotting If NUPU 2 one summary is plotted into the open diagram the axes are drawn the diagram is then closed to further plotting If NUPU 3 one summary is plotted into the open diagram which remains open to further plotting Two explanation blocks can be included The first one explains the symbols for the laminar separation bubble warning The second one provides brief definitions of the abbreviations T S U and L The explanation blocks are plotted by increasing NUPU by 4 in the CDCL line that initiates the diagram The second block is omitted if the option for inserting labels near the curves as described below is not exercised Thus if NUPU 4 or 5 a diagram is opened as with NUPU 0 or 1 and in addition the explanation blocks are plotted 6 7 1 Extension of Frame The upper and lower edges of the frame are determined when only the c values of the first summary i e CDCL line with NUPU 1 or 5 are available If NUPE 1 experimental data will be inserted late
65. ference between the natural logarithm of the local maximum amplification factor and the currently valid N entitled NDIFF if mpr 7 the local skin friction coefficient cr entitled CDsf s if mpr 8 the decimal logarithm of the Reynolds number Rs based on the displacement thickness and the local velocity V entitled LOG RD1 and if mpr 9 the product d times Rs which is important for the pressure gradient in the laminar separation bubble entitled D2 RD2 If only one MU R pair is specified three additional columns are produced containing the velocity outsinde of a present separation the slope dn ds of the maximum amplification function given as 61 dn ds and the maximum amplification function n s itself entitled UBD D1 dn ds and n s if suction is active the two last columns contain vp and cg desuignated VO and CQ if mpl 0 the diagram is suppressed if mpl i lt 5 the boundary layer development for the it MU R pair is plotted as Rs versus H see refs 1 and 3 Two plots are generated the left one is for the upper surface and the right one for the lower surface Each plot contains one curve for each a value in the preceding ALFA line The diagram is closed afterwards and if mpl 6 8 only the curves for the first MU R pair are plotted as follows if mpl 6 the diagram is opened the curves for the first MU R pair are plotted and the diagr
66. for the transition and separation curves is zr c and 15 c the ordinate ce The plotted arc lengths s c and sg c along the airfoil surface from the transition point and the separation point respectively to the trailing edge are thus s c gt 1 27 c and ss c gt 1 zg c A CDCL line normally follows an RE line but may also follow an FLZW or PLW line It should be remembered however that the Reynolds number varies with the lift coefficient in the latter cases The curves plotted correspond to the various chords c and for the FLZW line to the twist angles O as well The curves for the first MU R or c O pair specified in the preceding RE FLZW or PLW line are solid followed by up to five different types of broken lines each corresponding to a different pair The types of broken lines drawn can be changed The results from several CDCL lines can be plotted in one diagram as described for the DIAG line Chapter 5 6 and the STRK line Chapter 5 2 Because the frame dimensions must be determined when the diagram is opened if the diagram is to remain open for further plotting it may be necessary to specify a larger frame which is accomplished by means of the F numbers in the CDCL line that opens the diagram The minimum cg along the cg axis is not necessarily zero If the minimum drag coefficient in the results to be plotted by the CDCL line that opens the diagram is greater than 0 01 which occurs frequently for low Reynolds numbers the
67. form z c and y c where c is the chord R and T are ignored This is the most general coordinate reading option A total of NQ points are defined each one by x and y The points can be specified in two different sequences Both trailing edge points even if identical must be given If they are not identical the panel method will invoke a wake model The details of the sequences and the format of the coordinate lines are described in Chapter 4 1 4 NACA 6 Series Airfoils If NUPU 3 an NACA 6 series airfoil ref 8 is specified Only the thickness distribution is given the mean line and its slope are computed NQ is ignored The number of points is determined from the input coordinates A R and T specify the NACA 6 series mean line and a thickness ratio where A a which is the extent of the constant vorticity along the mean line i e the point where the vorticity begins to linearly decrease R c which is the design lift coefficient which determines the amount of camber T thickness factor normally T 1 The succeeding lines contain the coordinates of the upper surface of a symmetrical NACA 6 series airfoil from the leading edge to the trailing edge as presented in reference 8 The number of airfoil points VQ depends on the number of points for the symmetrical airfoil which is determined from the input The format of the succeeding coordinate lines is described in Chapter 4 1 4 It should be noted that the
68. he bubble model further improved the predictions over a wide range of Reynolds numbers 6 BOUNDARY LAYER ANALYSIS 45 6 2 EHNN Line The EHNN line specifies only the value of N EH NN Fi EHNN The default value of EH NWN is 11 The value of EH NWN remains valid until it is changed by another EHNN line 6 3 RE Line The RE line normally specifies up to five pairs of numbers each containing a transition mode MU and a Reynolds number R Boundary layer computations for each MU R pair are performed using the velocity distributions V x a for all the a values in the preceding ALFA line Single roughness elements can also be specified The code terminates if there is no ALFA line somewhere before the RE line The results from the boundary layer analysis are listed and plotted according to print mode mpr and plot mode mpl A summary of the results is stored in blank COMMON arrays CW SA and SU which remain available for other computations Other options in the RE line allow certain parameters to be specified without initiating a boundary layer computation 6 3 1 Print and Plot Modes If NUPA 1 8 mpr NUPE and mpl NUPI where if mpr 0 the listing is suppressed if mpr 1 the listing of the summary is produced which contains the lift drag and pitching moment coefficients including viscous corrections and drag from laminar separation bubbles the arc lengths of the turbulent and separated flows on both airfoil surfaces and a
69. he middle and highest drag curves coincide 6 BOUNDARY LAYER ANALYSIS 63 REMO1 PTEST FOR USERS GUIDE TRA1 115 54 1252627 128 329 6 2 11 2 12 550 14 60 3 TRA25 1415 52 7 68 4 13 52 3 68 1 3 0 18 3 ALFA 80246 8 10 12 14 16 RE 3 600 3 04 600 3 02 600 CDCL 15 6 213411211221 122 2310F O 1015SUl 2015U1 3015U1 NSU1 SU2 Z 15 8703Z TRA1 220 5526 5 2829 5 2 11 2 12 5 0 14 60 8 TRA25 2 4 20 5 2 7 68 4 16 5 2 3 68 1 3 0 15 87 ALFA 8 57 9 11 13 15 17 19 21 RE CDCL 6 21 9411 712530 21 9110F 1 4 1SU2 5 1SU2 6 15U2 The third example illustrates the insertion of experimental data fig 21 Note that the line ex TEST FOR USERS GUIDE SUI SU2 18 3 15 87 SUI R 0 6x10 Cr o AER SUI 0 6x10 without b d 7 I N iD ee aes SUI 0 6x10 with b d u we F ory Pe cas U2 0 6x10 A fs eas A U2 0 6x10 without b d dopo SU2 0 6x10 with b d u A 157 AA K IS m L x di I E 7 f A J NN 0 T T m E 0 5 10 10 Figure 20 CDCL plot for SU1 and SU2 airfoils planation for the experimental data ref 14 is given after 3 in the CDCL line although only two MU R pairs are specified Because bubble drag is likely for the given Reynolds number the computations have been performed with and without the bubble drag option It is unnecessary to specify the option for bubble drag from the upper surface only because the lower surface exhibits no bubbles within the lo
70. hich follows the C and at least one space The comment is written in the output listing 2 2 2 REMO Line The REMO line controls other general options 3 AIRFOIL DESIGN 4 NUPA NUPE and NUPI are ignored If the last digit of NUPU O all plots are rotated 90 counterclockwise The F numbers specify the line widths for plotting Different line widths are used for the curves and the axes in the plots The width specified by PENTI is used for the curves and by PENAX for the axes Subroutine FORMEL which draws the characters sets the line width to one tenth the character height This width is constrained by two parameters SM AX and FKK After plotting a character the line width is reset to the previous value The F numbers have the following meanings F SMAX which is the maximum line width of the labels the default value is 1 mm Fy FKK which provides a smooth reduction of the line width between SMAX and FKK x SMAX the default value is 0 4 F PENLI which is the line width of the curves the default value is 0 4 mm Fi PENAX which is the line width of the axes the default value is 0 25 mm A parameter is not changed if its input value is zero In the upper left corner of each plot Eppler 05 V and the date of the code version followed by Run and the current date and time are written The default height of this text is 4 mm In any column after column 14 or three columns after the last specifica
71. igit after the decimal point is a then the rounding is done to 3 a digits for K u K and j 3 AIRFOIL DESIGN 8 and to 2 a digits for a The latter is significant only if some of the a values are iterated see below Both F and Fx should specify the same value for a F specifies JT MOD which is the iteration mode used to achieve the desired value Kpr of Kg Fi specifies Kp which is the desired value of Ks Ky Ky Fi specifies Kio which is the tolerance on the achievement of Kpg Kio 0 normally The following iteration modes specified by F can be used to achieve the desired trailing edge angle as indicated by Ks lf IT MOD 0 no iteration is performed F and F3 are ignored and Ky and Ky are determined by the other design parameters If IT MOD 1 all a for the upper surface i lt iz are replaced by a Aa If IT MOD 2 all a for the lower surface i gt iz are replaced by a Aa If IT MOD 3 all upper surface a i lt iz are replaced by af Aa and all lower surface a i gt iz are replaced by a Aa For iteration modes 1 3 certain arcs can be excluded from the iteration by specifying a number b after the decimal point Thereby b arcs from the trailing edge forward on the corresponding surface are excluded from the iteration For example IT MOD 2 7 excludes the seven arcs on the lower surface forward of the trailing edge from the iteration If ITMOD 4 K is replaced by K
72. ilable for further plotting If NUPA 4 or 9 the results for the current polar are added to the arrays without first clearing them If NUPA lt 5 the axes do not necessarily include the zero points If NUPA gt 5 the axes include the zero points If NUPE 4 0 NUPE specifies the symbol number The symbols and their corresponding numbers are shown in figure 12 If NUPE 0 the results for the current polar are not stored If NUPA 4 0 all polars stored thus far are plotted as for NUPA 3 or 8 If NUPI 0 or even a speed polar is plotted If NUPI 1 or odd a power polar is plotted Several options for additional labelling are available as follows After N the airfoil name can be replaced by the given character string as in other diagrams 6 BOUNDARY LAYER ANALYSIS 53 After S a character string can be given that indicates the span The current span is inserted automatically following the explanation If only Suu is given the span and m are plotted i e the span is assumed to be in m After W a character string can be given that indicates the aircraft mass The current mass is inserted automatically following the explanation If only W 4 is given the mass and kg are plotted After A a character string can be given that indicates the wing area The current wing area is inserted automatically following the explanation If only A y is given the wing area and m are plotted After T
73. ined by two points one on the upper surface corresponding to y 0 and one on the lower surface corresponding to y 360 Moreover additional points are automatically inserted near the leading edge depending on its shape Thus NQ depends on the shape of the leading edge and is always greater than N The arc limit vi of the leading edge is not specified but rather computed by the code This is indicated in the input by setting v 0 The input data for the design method is contained in four line types The TRA1 line specifies the arc limits v and their corresponding a values The TRA2 line specifies the pressure recovery and closure contribution parameters the iteration mode and the amount of pressure recovery to be achieved by the closure contribution Ky Ky The RAMP line specifies two arcs on each airfoil surface by which a transition ramp can be defined The ABSZ line provides additional options A detailed description of the use of the input parameters in airfoil design is given in reference 3 3 1 TRA1 Line NUPA and NUPE are ignored NUPI and NUPU together specify the airfoil identification number i e up to four digits F specifies n F specifies aj in degrees relative to the zero lift line F3 Fi va a5 and so on A TRA1 line may contain up to 11 pairs v a Reading is terminated by the end of the DLFF sentence e g two spaces As many TRA1 lines as necessary can be given Up to 120 arcs are allowed f
74. ines which are not in the normal format In the first column they contain a single letter identifier L D M T A X Y or E Following the identifier they contain the Lift coefficients Drag coefficients Moment coefficients Transition locations x7 c or Angles of attack in degrees The E line terminates the experimental data Occasionally drag or transition data are given for a values instead of cg values The values must then be transformed into cg values which can be accomplished by means of Y lines The Y line contains oy values that are transformed into cz values using the preceding A and L lines Following the Y line D and T lines with A in the second column are permitted in which case the cg values are determined from the Y line not the preceding L line An X line is not necessary but is allowed and treated as a TA line All lines except the E line contain up to three DLFF sentences beginning in column 4 The first DLFF sentence normally contains N gt 1 experimental values as DLFF words For example Duu 0048 0049 00511 0060 007514 Preceding the DLFF sentence which contains five words in this example a DLFF sentence con taining only one word can be given This word specifies the factor by which all the words in the succeeding sentence are divided For example Di 10000 u48 49 51 60 75 5 which is equivalent to the previous example In many cases it is easi
75. inserted near the curves Both CDCL lines contain an F at the end which continues the DLFF words in column 1 of the next line There three spaces must be present to terminate the previous DLFF sentence Additional text can then be inserted in the third and fourth line explanations The option is used in the second CDCL line to include another line which in this case is not necessary Note that the text in the second line explanation specified by BF plots only an additional b The F normally causes the flap data to be inserted but in this case no flap data are available Also the error in the input NACA airfoil name 2301W is corrected because the name is determined from the input parameters REMO1 P FXPR 5 NACA 2301W 61 20 30 12 ALFA 802468 10 12 14 RE 3 1000 3 2500 CDCL 15 6 1 2521 35 1 6 1 04 10 21 1314 53F 1FB 2BF FLAP 25 5 3 10 ALFA 8 4 6 8 10 12 14 16 18 RE CDCL 6 1 921 812230 11 5110012 5F 3F 4F E1935 ENDE The second example illustrates the insertion of labels for two different airfoils SU1 and SU2 plotted in one diagram fig 20 This example also demonstrates the independent evaluation of the effect of laminar separation bubbles on the upper and lower surfaces Again LAU F 4 0 in the first CDCL line and the frame is extended by 0 6 to accommodate the expected higher ce values of the second 6 BOUNDARY LAYER ANALYSIS 62 T boundary layer transition S boundary la
76. ion for all values in the ALFA line without displacement iteration The displacement thickness is then smoothed and added to the airfoil contour for all values specified in the DPIT line and for all Reynolds numbers specified in the RE line The modified airfoil shapes are then analyzed using the panel method The resulting c amp and cm amp are stored The cq and ce values from the normal i e uniterated computation are listed and plotted only the a and c values are alterred If no displacement iteration is performed the viscous effects are assumed to reduce the lift curve slope from the potential theory value to 27 The displacement iteration determines this reduction 6 BOUNDARY LAYER ANALYSIS 66 from the displacement effect Therefore it is possible that the lift curve slope after the displacement iteration is greater than 27 which occurs in experiments as well The linear portions of the lift and moment curves are adapted to least squares fits of the values from the displacement iteration The correction due to boundary layer separation is then added see ref 1 The modified values a are listed in the boundary layer summary as AC If no displacement iteration is performed a a The least squares fits of the lift and moment curves are undefined if the displacement iteration is performed for only one a In this case the slopes of the curves are taken from the uniterated computations and only
77. isting headline from PANEL x y V listing m and cp listing headline vorticities and slopes from PANEL mpa for PANEL listing remains as before no x y V listing x y V listing mpa for PANEL listing remains as before Note that the print mode mpa cannot be set to 0 in an ALFA line This must be done in an FXPR or PAN line Setting mpa in the ALFA line i e NUPA 1 is only useful if the moment coefficients are to be listed NUPI and NUPU specify the details of the x y V listing and also the corresponding plot produced by a DIAG line If NUPI 0 the a values are relative to the zero lift line and the x y V listing and the DIAG plot contain velocity distributions If NUPI 1 the a values are relative to the x axis and the x y V listing and the DIAG plot contain velocity distributions If NUPI 2 the a values are relative to the zero lift line and the x y V listing and the DIAG plot contain pressure Cp distributions If NUPI 3 the a values are relative to the x axis and the x y V listing and the DIAG plot contain pressure C distributions If NUPU 0 22 NUPU specifies na which is the number of F numbers i e values to be read The number of F numbers n is determined from the input If n gt Nna Na is set to n Thus it is simplest to set NUPU to 1 and let the code count the a values If NUPU gt 22 a listing containing only the point numbers x y and y is produced and na is set to 0 If NUPU 0 NUPI
78. l step of the conformal mapping This is transparent to the user The results may however differ slightly from those of older code versions mainly for airfoils with very sharp leading edges Those lines in previous data sets that specify additional points near the leading edge e g TRA1 lines with F gt 998 need not to be deleted they are now simply ignored Figure 2 shows the leading edge of a very thin airfoil with N 60 in the TRA1 line with and without additional points near the leading edge Note that the shape without additional points cannot be generated using the current version of the code The computed airfoil points are identified on both airfoils by tic marks perpendicular to the airfoil surface see STRK Line Chap 5 2 Figure 2 Thin airfoil with and without additional points near leading edge 3 AIRFOIL DESIGN 11 3 3 RAMP Line The RAMP line allows transition ramps to be designed without specifying several arcs with different a forward of the pressure recovery Instead the length of the pressure recovery function as specified by A in the TRA2 line is extended forward by Av The recovery function between the trailing edge and A Av which is the aft end of the ramp is not altered The shape of the ramp is determined by Av and Avy Over the length of the ramp which extends from A Av to A Av the recovery function is replaced by a parabola with an inclined axis of symmetry The parabola smooth
79. layer is initially stable During its development a combination of Reynolds number and shape factor must be found for which the first TS wave becomes unstable This stability limit has been evaluated for many shape factors A table was then constructed that allows the stability limit for a given boundary layer development to be evaluated precisely by interpolation This evaluation also yields the frequency of the first unstable TS wave The amplification rate of a TS wave depends on the local Reynolds number and the shape factor of the boundary layer flow in which it develops and on its frequency An amplification table must therefore contain values depending on three parameters In stability theory these three parameters are the Reynolds number based on the displacement thickness the shape factor H and a nondimensional frequency 3 The current amplification table contains more than 40 000 values The boundary layer computation begins with the search for the first unstable TS wave with its nondimensional frequency Berig This yields also the natural frequency ferit A frequency range with 64 frequencies f is defined around ferit For all fi the amplifications are evaluated and their natural logarithms are summarized into the amplifications Ina s At any position s along the airfoil surface the maximum amplification n s max ln a s is evaluated by quadratic interpolation If m reaches the specified value N transition is assumed D
80. le for Strake E AE a Example for Strake SUPER Y 7 76 SUPER Y 7 76 gt ON SUPER X 8 0 i SUPER X 8 6 O Figure 8 Two diagrams from example for STRD and STRK lines which contains the x axis and the labels The distance between the chord lines is 14 mm The succeeding STRK line plots the airfoil with chords of 150 and 140 mm and leaves the diagram open to further plotting The name of the first airfoil is set to SUPER X Then a second airfoil is computed and plotted with chords of 150 and 140 mm its name is set to SUPER Y and the diagram is closed Note that the second STRD line is valid for more than one STRK line 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 26 5 3 MACH Line The MACH line initiates two runs of the panel method the first one with the original coordinates of the airfoil and the second one with a new set of coordinates in which the ordinates y c are multiplied by the factor 8 y1 M Following a MACH line all velocity and pressure computations consider the compressibility effects according to the method of reference 11 including the listing of the velocity or pressure distributions after an ALFA line the plot of the velocity or pressure distributions after a DIAG line and all boundary layer computations NUPA NUPE NUPI and NUPU are ignored F M which is the Mach number The default value is 0 Contr
81. mber on the original airfoil aaa of succeeding F must decrease If the minus sign is given aaa is replaced by NQ aaa and the points are deleted relative to point NQ which is the last point This is useful on the lower surface All negative F must occur before positive ones Only the first positive F may have a greater aaa than the last negative F For example FLAP uuuuti 8 08 5 2 01 which deletes points NQ 8 through NQ 5 and 2 and 3 If NUPU 2 points are inserted on the upper surface F 10021 c Fy 100y c F Fa 100x2 c 100y2 c and so on The new points are inserted in the correct sequence between or aft of the points remaining after the deletions resulting from the FLAP line with NUPU 1 The sequence of the points to be inserted is arbitrary For example FLAP uuuu2u120 7511 10 2 which inserts two points that extend the upper surface x c 1 10 y c 0 02 and z c 1 20 y e 0 05 If NUPU 3 points are inserted on the lower surface For example 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 29 FLAP 3100 2 5 120 5 which inserts two points that extend the lower surface x c 1 00 y c 0 0250 and z c 1 2000 y c 0 0500 Normally some points must be deleted by a FLAP line with NUPU 1 before new points are in serted If NUPU 4 or 5 additional points are splined in The F numbers are interpreted just as they are for the FXPR line including the opti
82. ment 2 V 15 4 36 3 25 Flap 15 0 Flap relative to the x axis 0 5 17 9 oe US88 07 T T 0 0 5 x c 1 Figure 14 Velocity distributions for unflapped and flapped US88 airfoil REMO1 P TRA1 1111 0 5 60 5 TRA2 1111 4 17 5 2 1 7 4 17 5 2 1 73 200 ALFA 10 DIAG 101 6 FLAP 9 25035 ALFA 1001 O DIAG 3 1 123 Z01Flap FLAP 8 1 49 2 10 ALFA 1001 O DIAG 2 1 42 Z 1Double Flap 39 The FLAP lines of this example are the same as the last two FLAP lines in the example for listing the moment coefficients The velocity distributions for three shapes are plotted in one diagram by NUPU 1 3 and 2 Only one a value is given This value is included in the explanation line and omitted from the labels near the curves The additional text given after Z is plotted at the location given by the group of three numbers Using 1 instead of Z would have the same effect The third example illustrates the smoothing option for Wortmann airfoils The velocity distributions for the original coordinates and those after three smoothings are shown in figure 16 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES Double Flap 0 relative to the x axis Figure 15 Velocity distributions for airfoil 1111 unflapped and with single and double flaps FXPR FROM THE NEW BOOK FIG 13 FX 63 137 FX63 13701 000 000 82 40 249 169 501 373 818 630 1189 FX63 137 7 1601 1219 2043 1514 2516 1794 3018 2052 35
83. ment gt is increased by an amount that depends on the height of the element and the local shape factor If the boundary layer is laminar at the location of the roughness element transition is assumed to occur at that location and dp is not increased 6 BOUNDARY LAYER ANALYSIS 44 6 1 2 Profile Drag The profile drag coefficient cy is calculated after each boundary layer computation This is usually performed according to the Squire Young formula 5 112 te Vie 2 ca bare 1 3 The subscript te denotes at the trailing edge In previous versions of the code this formula was modified for separated flows by using instead of H12 se Hi min Hiro te 2 5 4 An upper limit for H12 te had to be introduced that was relevant mainly if the turbulent boundary layer separated early when U was high Recently a new formula A A pan 1 ES MA E Ki H 3 t6 Cd 2 02 t6 1 E k l E A 5 was developed ref 5 where Vie A 6 pe 6 and amp is a parameter that cannot be determined precisely For x 0 7 this formula yields drag coefficients that in normal cases deviate little from those resulting from the Squire Young formula and it does not require modification for early separation The shape factor Hy e is limited to its value at separation only if Vie lt V gt This formula now replaces equation 3 It can as was possible with the old formula be applied during the computation of the boundary layer where it in
84. ne exercises four options First the shape of an airfoil can be altered to correspond to that due to the deflection of a simple flap Because the panel method does not allow sharp corners in the airfoil surface a transition arc between the flap and the forward portion of the airfoil must be introduced Such a transition arc occurs naturally on the convex side of a real wing but not on the concave side where a corner is formed This concave corner however is smoothed by a locally separated region and therefore it is reasonable to introduce a transition arc there as well This option is initiated by NUPU 0 The second option allows the analysis of chord increasing flaps It should be noted that while the airfoil shape that results from this variable geometry option may have an increased chord it does not contain a slot and thus is still a single element as opposed to a multielement airfoil This option is initiated by NUPU 1 5 The third option specified by NUPA 0 allows the modification of single points on the airfoil The fourth option specified by NUPI 0 concerns only the reference point for the hinge moment For all options that modify the shape of an airfoil if NUPE gt 8 the modified airfoil replaces the original one In this case the original airfoil is completely lost and the new modified one can be further modified by additional FLAP lines In this way it is possible for example to introduce a secondar
85. nge moment coefficients for the spec ified angles of attack these coefficients also remain available for other computations and additional listings specified by print modes mzy mpa and mcm One last option which lists the second derivatives of the velocity or pressure distributions at various angles of attack is described at the end of this section NUPA and NUPE determine the print modes If NUPA 0 mzy mem and mpa remain as previously set If NUPA 4 0 may NUPE and mcm NUPA If NUPA 1 mzy NUPE mcm NUPA and additionally mpa NUPE 1 If may 0 the airfoil coordinates and the velocity or pressure distributions for all the specified up to 14 are listed This is called an x y V listing If may 0 no listing is produced If mem 1 the pitching moment cm and hinge moment c coefficients for all the specified values are listed If mcm 1 no listing is produced If mpa 0 no listing from Subroutine PANEL is produced If mpa 1 or 2 only the headline from Subroutine PANEL is listed If mpa gt 3 the headline the airfoil coordinates and the vorticities for a 0 and a 90 from Subroutine PANEL are listed The default values are mzy 1 mcm 1 and mpa 1 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 34 The print modes are summarized in the following table ignored x y V listing as before Cm and c listing headline from PANEL no x y V listing x y V listing m and c l
86. normally omitted or 0 a is the transition mode a 1 or 2 i e fixed transition is no longer valid having been superseded by single roughness elements a 3 specifies natural transition a gt 3 specifies free transition with roughness factor r a 3 c is the bubble drag mode c 0 computes the bubble drag on both the upper and lower surfaces and does not plot warning triangles in the CDCL diagram c 1 computes the bubble drag on both the upper and lower surfaces and plots warning triangles in the CDCL diagram c 2 computes the bubble drag on the upper surface only and does not plot warning triangles in the CDCL diagram c 3 computes the bubble drag on the lower surface only and does not plot warning triangles in the CDCL diagram and c 4 does not compute the bubble drag on either the upper or the lower surface and does not plot warning triangles in the CDCL diagram In this case previous data sets now yield different results The natural transition mode MU 3 now specifies transition prediction using the e method and inclusion of bubble drag on both surfaces 6 3 3 Single Roughness Elements The single roughness elements have two different effects If the boundary layer is turbulent at the location of the roughness element 02 is increased by an amount that depends on the height of the element and the local shape factor If the boundary layer is laminar at the location of the roughness element transition is
87. nts near the leading edge or a transformation of the coordinates The new points are spaced equidistantly along the straight line between the two original points if c gt 5 Otherwise the points are spaced such that in x c 1 cos p 2 the differences between the angles y corresponding to the new points are equal i e equian gular spacing In previous data sets no more than nine points could be splined in between two original points and usually c 00 was used for equiangular spacing and c 99 for equidistant spacing Such data sets are still processed correctly The insertion of additional points frequently improves the accuracy of the results if portions of the airfoil have sparsely distributed points Near the trailing edge where the velocity changes rapidly the new points should be spaced equiangularly This option must be exercised carefully however The indices of all the points in arrays X and Y falling after the inserted points are increased by the number of inserted points The simplest way to avoid confusion is to specify the F numbers with decreasing values of a Thus a in F should be greater than a in Fy which should be greater than a in F and so on The same is true if negative F are used for the lower surface For example the NACA 6 series airfoils are defined by 26 points on each surface which results in a total of 51 points with the leading edge at point 26 One of the two identical leading edge points is
88. o cj If Fy lt 0 F 100c E3 F4 n cz or ch up to Fo Fio For example RE QS tu 8124171 5 131 2 performs interpolations for each succeeding boundary layer computation and the following results are listed for the first MU R pair cq at ci 0 8 for the second MU R pair cy for c 0 015 and for the third MU R pair cq at cp 0 2 To obtain precise results the values in the preceding ALFA line should result in a cg or cy close to the specified c or cp 6 4 FLZW Line The FLZW line initiates aircraft oriented boundary layer computations where the Reynolds number R varies with the aircraft lift coefficient Cz and the local chord c A local twist angle O which must be specified relative to the zero lift line of the entire wing can also be given The a values in the preceding ALFA line are taken as the local angles of attack relative to the zero lift line If the a values in the ALFA line are specified relative to the chord line they are converted to a relative to the zero lift line by adding the zero lift angle before these computations Thus the aircraft lift coefficient is Cr 0 11 a O 7 and the aircraft speed is gt 8 VCL where _ gm 9 v pS is the aircraft speed at Cz 1 g is the acceleration due to gravity in m s m is the aircraft mass in kg p is the air density in kg m and S is the wing area in m To prevent v from reaching unrealistically high values as C approaches
89. oil design is performed by a conformal mapping of the outside of a circle in the plane to the outside of the airfoil in the z plane Accordingly the airfoil design is specified by several arcs on the circle with limits y having a values of a and the parameters for the pressure recovery functions and the closure contributions including Yw Pw Ys and ps The computation is based on N equiangular points on the circle The value of N is specified and must be divisible by 4 The arc limits y as well as Yu Pu Ys and Ps are not specified in degrees but instead relative to the point numbers Thus Ay 21 N 360 N 1 and w pi Ap A pw Ap Gw Ay v ys Ay Mv Ps Ay 2 A practical value for N is 60 Thus Ay 360 60 6 In this case v 15 specifies an arc limit that corresponds to a point near midchord on the upper surface of the airfoil whereas v 30 is near the leading edge and v 45 is near midchord on the lower surface If v is an integer number the arc limit normally corresponds to a point on the airfoil If v is a decimal number the arc limit falls between two points on the airfoil The same is true for the A values which specify the beginning of the pressure recovery and closure contribution regions Symmetric airfoils of course have A and The number of points on the airfoil NQ differs from N Most points correspond to the equiangular points on the circle The trailing edge however is def
90. ollowing example plots two different airfoils in one diagram TRA1 and TRA2 lines first airfoil STRD 1 500 5 STRK 1 500 TRA1 and TRA2 lines second airfoil STRK 1 500 0 5 Both airfoils have a chord of 500 mm and are separated vertically by 5 mm The chord lines of both airfoils are plotted and the diagram is terminated by the second STRK line If the second STRK line had specified NUPU 0 the chord from the preceding STRK line would have been used and the diagram would have remained open to further plotting The following example produces the diagrams shown in figure 8 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 25 REMO1 PO1OREO2XAMPLE OF AIRFOIL PLOT TRA1L 1 28 5 3 0 10 60 2 TRA24 1418 5 2 1 7 418 5 2 1 76 30 STRD 1 32 5 f 15 STRK 2 150 100 1 STRD 1 62 14 016 15 STRK 2 150 140 NSUPER X TRA1 2 27 5 5 0 10 60 5 TRA24 2418 5 2 1 7 418 5 2 1 76 3 0 STRK 1 150 140 1 NSUPER Y The first diagram fig 8 contains only the first airfoil with two chords 150 and 100 mm and is closed by the chord of 0 1 mm which is not plotted The vertical distance between the airfoils is 1 mm and the x axis and the labelling of the airfoils are suppressed by NUPU 1 and F 1 in the STRD line The line width is set to 0 15 mm by Fy in the STRD line Only the labelling specified in the REMO line is plotted The second STRD line with NUPU 1 and F 0 016 initiates the second diagram fig Examp
91. omitted The points near the trailing edge i e 7 c 1 00 x2 c 0 95 and x3 c 0 90 as well as those near the leading edge are too widely spaced to obtain accurate results from the panel method FXPRuuuuu3u502 491 261 9 251 9 21 12 FXPRuuuuu3u7251 9 21 12 251 9 21 12 FXPRuuuuu3u2501 5 201 4 102 4 2501 5 201 4 1102 4 All three lines have the same effect The second and third lines use the option of negative F The third line uses two columns for b i e two digits which is not necessary in this example The last 4 POTENTIAL FLOW AIRFOIL ANALYSIS 17 two lines also function correctly if a new point was inserted at the leading edge using NUPI 0 the first line would have to be changed in this case In this example two points are inserted on each surface between z c 0 95 and 1 00 in the equian gular spacing mode one point on each surface between z c 0 90 and 0 95 in the equiangular spacing mode and one point between the leading edge and the first point on each surface in the equidistant spacing mode Thus a total of eight points is inserted Another example is given in the next section under the specification of Wortmann airfoils 4 1 3 Input of Coordinates Subroutine FIXLES delivers the coordinates of an airfoil to be analyzed In the FXPR line NUPU specifies the option The line after the FXPR line is always required It contains the airfoil name up to 12 characters followed by two spaces and then one D
92. on of negative F F aab dd If NUPU 5 in addition to the splining in of points a transformation is performed that ro tates the modified airfoil around x 0 y 0 and stretches it so that the first point becomes x c 1 y c 0 The option NUPE 9 can also be used Care must be exercised because deleting points i e NUPU 1 as well as inserting new points i e NUPU 2 or 3 changes the sequence numbers of the points and the total number of points NQ For splining in additional points the alterred point numbers must be taken into account An example is given in figure 10 For example FLAP Uuouuu4u 7 24u 162227113 which inserts a total of 15 points all with equiangular spacing four points between points NQ 2 and NQ 1 six points between points NQ 1 and NQ two points between points 2 and 3 and three points between points 1 and 2 The application of the four FLAP lines given in this section to an NACA 23015 airfoil defined originally by 61 points is shown in figure 11 The following steps occur The original upper surface is maintained up to the original trailing edge although some points near the original trailing edge are deleted because the close spacing there is no longer necessary although it is near the new trailing edge a c 1 20 y c 0 05 as described below On the lower surface points NQ 8 through NQ are deleted which includes the lower surface trailing edge point On the upp
93. or each airfoil design 3 AIRFOIL DESIGN 6 The number of points on the circle comes from the last arc limit v N This number must be divisible by 4 and no greater than 120 The leading edge arc limit must be specified by v 0 The value of v which is computed by the code must fall between 1 and 1 41 Thus if 1 1 is too large or 1 41 too small no solution for v i can be found In this situation the code writes a message and then stops The same is true if a7 gt aj It should be remembered that arc limits can be specified that do not correspond exactly to the points on the airfoil Indeed arc limits that fall between points e g 1 16 5 yield velocity distributions that are slightly smoothed An example of a TRA1 line is TRA1 1098 23 5 8 27 5 10 0 112 60 2 1 C MIT SAILPLANE This line results in Ay 6 and therefore If vi lt 1 1 then v is interpreted as Av and v 1 1 Av is set This option is particularly convenient if as discussed in reference 3 many arc limits are used having Av 2 and the arc limits fall between the airfoil points Using this option the above example can also be specified by TRA1 1098 23 5 8 4 110 10 112 6012uu The value of a for each arc S 11 lt v lt vi will be computed if Q given apr This is performed by the following option LL is specified for a If for the arc S a gt 90 is input Q is set to a 90 and aR to a for the up
94. per surface or a for the lower surface and a is computed such that Q occurs in the middle of S for a ap This option was previously used to specify transition ramps They are now much more easily specified using the RAMP line Chap 3 3 3 2 TRA2 Line The TRA2 line specifies the main pressure recovery on each surface the length of the closure contribution necessary to achieve a closed airfoil shape and optionally the addition of identifying letters to the airfoil name The main pressure recovery is determined by a function w x by which the velocity distribution along the upper surface as defined by the a values is multiplied The function has a value of 1 forward of the beginning of the recovery which is specified by A for the upper surface and A for the lower surface The recovery itself is computed using two parameters K and u where K determines the amount of recovery w and y determines the shape of the recovery The combined effect of K and u is complicated Therefore the recovery can be specified by other more explicit parameters e g yu and w see figure reframpm as well 3 AIRFOIL DESIGN 0 3 YH 0 3 0 4 0 5 0 6 0 7 0 8 09 x 1 Figure 1 Effect of u on recovery shape If NUPA gt 0 the airfoil number will be prefixed by one or two letters with or without a space between these letters and the air foil number as shown in the table to the right If 8 followed by two letters are given in a TRA2 or RE
95. ption NUPI 1 is useful in two specific cases It can be used to determine the aerodynamic center for which c is constant with and the value of c can be used to evaluate the bending moment of ribs in a wing The options NUPI gt 3 are relevant only in conjunction with other FLAP lines because the values Of Cm and c would otherwise be identical These options can be exercised however after a FLAP line with NUPE 9 Another FLAP line then allows another flap to be introduced and the moment relative to the previous reference point e g the previous flap hinge point to be computed The authority of Flettner flaps or trim tabs can thus be analyzed The following input lines produce the listing below REMO1 PLISTING CHAPTER FLAP LINE ALFA FXPR 4 FLAP 9 25035 NACA 0009 61 0 o 09 ALFA101003 10 O 10 ALFA101003 10 0 10 FLAP 3 FLAP 1 26 148 0 ALFA101003 10 O 10 ALFA FLAP 8 1 49 2 10 FLAP 2 40 0 ALFA101003 10 O 10 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES PANEL METHOD NACA 0009 9 Airfoil NACA 0009 9 Moments delta 0 deg Hinge at x 0 y 0 Alpha relative to the chord l ALPHA CM CH CL CL LIN 10 00 0 013212 0 301082 1 168387 1 100000 0 00 0 000000 0 000000 0 000000 0 000000 10 00 0 013212 0 301081 1 168386 1 100000 Airfoil NACA 0009 9 Moments delta 0 deg Hinge at x 0 26148 y 0 Alpha relative to the chord l ALPHA CM CH CL CL LIN 10 00 0 000007 0 111141 1 168387 1 100000 0 00 0 000000 0 000000 0 0
96. r Additional CDCL lines with NUPU 2 or 3 may plot summaries in the same diagram that include cy values that exceed the minimum or maximum cz of the first summary Therefore F Fs of the CDCL line opening the diagram i e NUPU 0 1 4 or 5 allow the frame to be extended and the key in the upper left corner to be shifted First Co max mazde Fy 18 Cl min Mind ce Fs are evaluated Thus F4 and Fs specify the minimum ce range which may be extended by the co but not reduced Both Ce max and Ce min are rounded to one digit after the decimal point to coincide with the tic marks at along the cy axis The default values are F4 F 0 Then F F3 allow the upper and lower edges Ce up and Ce iow Of the frame to be shifted relative to C max ANd Comin respectively F shifts the key in the vertical direction F gt 0 shifts it up Fi lt 0 shifts it down Fm max F Fz extends the upper edge cy of the frame F extends the lower edge ce iow Of the frame Chup Cmax Max F 0 4 Fm 0 15 0 41 BF 19 Celow min 0 25 comin 0 15 F3 where BF 1 if the explanation blocks are to be plotted and BF 0 otherwise The values of Fm and F3 should be as large as the amount by which succeeding ce exceed Ce maz and Comin 6 BOUNDARY LAYER ANALYSIS 57 6 7 2 Labelling Without additional input the axes are labelled and the airfoil name is plotted in the upper left corner After the name the thi
97. r Input and Flow Chart 7 1 Input Line Sequence aoaaa a A A ari A de 7 2 Flow Chart References 35 36 36 40 41 41 42 44 44 45 45 45 46 47 48 49 49 50 53 55 56 57 58 60 60 61 61 65 68 68 70 71 1 PRINCIPLES OF CODE 1 1 Principles of Code The sequence of execution within the code is controlled in a flexible manner by the input lines themselves Each input line has a name in the first four columns Thus an ALFA line has ALFA in the first four columns and an RE line has RE i e RE followed by two spaces The spaces are part of the name and therefore those two columns must not be used for other purposes The code reads the name and then branches to the corresponding section of the code After performing the computations printing or plotting initiated by the input line the code returns to the main routine and reads the next input line In effect the code is asking What should do next Some of the lines initiate computations printing or plotting that requires results generated by other lines Thus the sequence of the lines is not completely arbitrary see Chap 7 Normally the data read from a line remain in effect until new data are read from a line having the same name Exceptions to this rule are described in detail Every input case must be terminated by an ENDE line During the development of the code many new options have been introduced The modifications
98. r the end of the last DLFF sentence The name must be terminated by two spaces Thus the name cannot contain two successive spaces 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 38 After Z a character string can be given that will be plotted after the label s explaining the first a value After i where i 1 2 9 a character string can be given that will be plotted after the label initiated by the th group of three numbers If only one a value is valid its value is omitted in the label s along the curve If i lt 30 li 30 specifies the number of the a value and the cy value is written near the curve instead of the a value This is normally done in the first group This option is useful if the Mach number is not zero The a label is then omitted If F is the last character of a character string the current flap data are plotted as c Flap 0 where cy is the flap chord and 0 is the deflection These data are not plotted if 0 0 The input iF or ZF adds only the flap data to the labels Font 1 see ref 6 is the default font for the airfoil name and therefore switching to capital Latin letters is superfluous in this case Experimental Data Experimental data can be inserted into an x y V diagram If NUPE 1 in the DIAG line that opens a diagram i e NUPU 0 or 1 the succeeding lines which have X Y or E in the first column specify the experimental data as follows
99. rd Betty F Experimental Results for the Eppler 387 Airfoil at Low Reynolds Numbers in the Langley Low Turbulence Pressure Tunnel NASA TM 4062 1988
100. read by a separate subroutine FIXLES which is called when an FXPR line is read This subroutine reads or generates the coordinates and writes them into blank COMMON arrays X 121 and Y 121 in the appropriate sequence i e from the trailing edge forward along the upper surface around the leading edge and back along the lower surface to the trailing edge The number of points NQ lt 121 is stored in the blank COMMON variable NQ Once the coordinates are available the slope of the upper surface 6 near the trailing edge is written into variable DLT in COMMON PRAL the lower surface slope 6 into DLTU These slopes are defined such that for symmetric airfoils s 6 Because many airfoils are not very smooth in the region surrounding the trailing edge a point x yi on the upper surface and a point x y on the lower surface are selected such that x c 0 9 and x c 0 9 Then dus yi Cc zi and On y c z3 are set These values are used when the lift and pitching moment coefficients are corrected for boundary layer separation effects Once all these values have been provided by Subroutine FIXLES the panel method is invoked Arrays X 121 and Y 121 are not changed The resulting vorticities which in the present notation are identical to the velocities for a 0 and a 90 are stored in arrays VF 121 and ARG 121 respectively Thus all the data are available to function VPR which computes the velocity a
101. reference 7 The total number of points NQ is determined from the input If NUPU 2 the pairs can be input in two different sequences the normal sequence used in the code i e from the trailing edge forward along the upper surface around the leading edge and then back along the lower surface to the trailing edge or from the leading edge to the trailing edge on the upper surface and then from the leading edge to the trailing edge on the lower surface The code reorders the latter into the normal sequence If NUPU 3 the pairs start at the leading edge as presented in reference 8 4 2 PAN Line The PAN line switches from the design to the analysis mode and therefore is required if the panel method is to be employed following a design i e TRA1 and TRA2 lines The PAN line contains the same options for the print mode and the insertion of points as does the FXPR line A cascade can also be defined in a PAN line 4 2 1 Switching from Design to Analysis Mode If 0 NUPA 0 8 NUPE and NUPA together control the print modes see FXPR Line Chap 4 1 NUPI controls the coordinate transformation see FXPR Line Chap 4 1 NUPU is ignored The F specify the additional points to be splined in see FXPR Line Chap 4 1 4 POTENTIAL FLOW AIRFOIL ANALYSIS 21 4 2 2 Cascades If NUPA 9 the parameters of a cascade fig 6 are specified by F F4 where F Az c F gt Ay G F3 ne which is the number of ca
102. rs i ER e i ER can be given Each group initiates labels to be inserted near the corresponding curves Corner e of the label a a is located near the point where Rs R along the curve for the ith angle of attack a see DIAG Line Chap 5 6 If is given without a minus sign the label a is omitted If e gt 4 corner e e 4 is located near the same point and the Reynolds number is plotted instead of a If the specification for the last curve is made with e gt 4 a is substituted for R in the headlines The plot for the upper surface is labelled if the sign of R is positive a minus sign initiates the labelling of the plot for the lower surface If NUPA 9 and F 0 F is the width in mm of the boundary layer development diagram The default width is 208 mm No boundary layer computation is performed This width remains valid until another RE line with the same option is given 6 BOUNDARY LAYER ANALYSIS 49 6 3 5 Interpolation of Drag and Lift Coefficients A RE line with NUPA 8 initiates in succeeding boundary layer computations drag coefficients Ca for given cf or vice versa to be evaluated by interpolation no boundary layer computation is performed The interpolation is performed for each boundary layer computation initiated following this line F specifies the number n of the MU R pair in the RE line or the twist angle chord pair in the FLZW line to be considered If Fs gt 0 F
103. s of vectors The vectors are not actually plotted but rather like all graphic output written to a file that must be postprocessed A description ref 6 is provided with the user s guide 1 3 Date and Time Most computer operating systems provide a calendar and a clock To distinguish different results the date and time are given in the output listing and in the plots The delivered executable version of the code provides the date and time from the corresponding operating system 2 Overview of Input and General Options 2 1 Overview of Input Lines The input lines can be segregated into the four categories design potential flow analysis options for both design and analysis and boundary layer analysis The function of each input line is summarized in the flow chart in Chapter 7 2 The line names can be given in upper or lower case letters Thus TRAI and tral are equivalent Mixed case is not permitted however Thus Tral cannot be given e The input lines for the general options are described in Chapter 2 2 e The input lines for airfoil design are 2 OVERVIEW OF INPUT AND GENERAL OPTIONS 3 TRA1 line which specifies the arc limits and their corresponding a values TRA2 line which specifies the pressure recovery and the closure contribution as well as the options for the trailing edge iteration RAMP line which specifies the transition ramps and ABSZ line which specifies a factor by which the number
104. s the corner that would otherwise occur at the beginning of the recovery function Several examples of transition ramps are given in figure 3 where the broken line is the recovery function from the TRA2 line without a ramp and the solid line with a ramp The ramp is specified by Av and Av only These parameters are angles on the circle in the conformal mapping It should be remembered that the length in x c between equiangular points is smaller near the leading and trailing edges and larger near midchord Figure 3 illustrates the ease with which the shape of the ramp can be controlled For example on the upper surface of aircraft wings the maximum curvature should usually occur toward the aft end of the ramp because boundary layer transition occurs there at lower lift coefficients and higher Reynolds numbers The opposite is true for the lower surface Controlling the curvature is accomplished by changing Av and or Avs Decreasing Av increases the curvature of the ramp at its aft end and vice versa increasing Av has the same effect The first four plots illustrate this effect for a recovery function with u 1 which is only slightly concave The last four plots show the same effect for a recovery function with u 0 25 which is very concave and initially very steep Clearly the shape of the recovery function must be considered when designing the ramp For concave recovery functions if Av is too small the intersection of the tangent to the re
105. scade members and F c which is the chord in mm If Fy 0 a diagram e g fig 6 is produced in which the current airfoil is plotted twice with the chord specified by Fy The horizontal and vertical distances between the two airfoils are Ax c and Ay c respectively The distance between the cascade members is defined by Ax c and Ay c as shown in figure 6 A Figure 6 Cascade parameters finite number of cascade members must be specified by F3 A PAN line with NUPA 9 merely stores the cascade parameters and does not invoke the panel method which must be done by another PAN line with NUPA lt 9 The computation of cascades is a generalization of the panel method When an individual airfoil is analyzed vorticity distributions are placed along the surface of the airfoil The distributions are determined such that the flow conditions on the airfoil surface are satisfied When a cascade of airfoils is analyzed the vorticity distributions must be placed on all members of the cascade and the amount of vorticity is again determined from the flow conditions on the surface of each member A cascade is usually assumed to have an infinite number of members in which case the flow conditions are satisfied on all members if they are satisfied on one member For infinite cascades a higher order panel method cannot be developed with closed formulas This is only possible with simple low order panel methods To maintain higher order precision th
106. spacing of the points as given in reference 8 is not very suitable for the panel method The option for splining in additional points should be exercised not only near the trailing edge but also near the leading edge An appropriate example is given in Chapter 4 1 2 NACA 4 Digit Series Airfoils If NUPU 4 an NACA 4 digit series airfoil ref 9 is specified The airfoil name e g NACA 4415 is given in columns 1 9 followed by two spaces and then the total number of points VQ to be computed A R and T are ignored 4 POTENTIAL FLOW AIRFOIL ANALYSIS 19 No other lines are required The necessary airfoil parameters see ref 9 are derived from the airfoil number given in columns 6 9 NACA 5 Digit Series Airfoils If NUPU 5 an NACA 5 digit series airfoil ref 10 is specified The airfoil name e g NACA 23012 is given in columns 1 10 followed by two spaces and then the total number of points NQ to be computed A R and T are ignored No other lines are required The necessary airfoil parameters see ref 10 are derived from the airfoil number given in columns 6 10 The NACA 5 digit series airfoils having reflexed mean lines i e the third digit is 1 cannot be generated For these airfoils the general coordinate reading option i e NUPU 2 must be used It should be noted that the coordinates presented in references 8 and 10 for the NACA 5 digit series airfoils contain minor inaccuracies and th
107. stributions for original and smoothed FX 63 137 airfoil Columns 1 5 in each output line contain the airfoil name If this name comes from the analysis mode characters 3 7 of the name are used If this name comes from the design mode a space followed by the four digits of the airfoil number are used Columns 6 8 contain the number of the first point written in that line Columns 9 80 contain four groups of three numbers each which are the z c y c and 8 values for one point No decimal points are written The x c and y c values in this file can be read using format F6 5 and the values format F6 4 6 Boundary Layer Analysis 6 1 Fundamentals The computation of the boundary layer development is performed by means of an integral method see ref 3 This method requires as input the Reynolds number R and the potential flow velocity distribution U s where s is the arc length from the stagnation point along the surface of the airfoil The velocity distributions are computed in either the design or the analysis mode The basic results of this approximate method are the momentum thickness d2 s and the shape factor Hz2 s Also the displacement thickness 6 s and the shape factor Hy2 s are evaluated The momentum thickness is most significant for the viscous drag the shape factor indicates the shape of the boundary layer profile Increasing H32 corresponds to a more favorable pressure gradient All results together allow the approximate evalua
108. t every airfoil point for every angle of attack 4 1 FXPR Line The FXPR line specifies the print mode mpa for the results of Subroutine PANEL how the airfoil coordinates are provided from the subsequent lines and an option for inserting additional points along a spline fit of the original airfoil points If NUPA 0 the print mode mpa remains unchanged the default value is 1 If NUPA 4 0 mpa NUPE where mpa 0 suppresses the listing 4 POTENTIAL FLOW AIRFOIL ANALYSIS 15 mpa 1 or 2 lists only the headline containing the lift coefficients for 0 and 90 angle of attack and the zero lift angle and mpa gt 3 lists the headline plus the coordinates the vorticities for 0 and 90 angle of attack and the surface slopes NUPI controls a coordinate transformation after which the leading edge is at x 0 y 0 and the tangent at this point is vertical The trailing edge i e the midpoint between the two trailing edge points is transformed into z c 1 y 0 The transformation generates a new leading edge point for all nonsymmetrical NACA and Wortmann airfoils which increases the number of points NQ by 1 If NUPI 0 no transformation is performed If NUPI F 0 the transformation is performed after the coordinates are read and possibly smoothed NUPU N 10S N S lt 9 IF S gt 0 the coordinates are smoothed The value N controls the derivation of the airfoil coordinates from the subsequent line or lines A summ
109. th NUPU 1 Point numbers after deleting points by FLAP line with NUPU 1 and before in serting points by FLAP lines with NUPU 2 and 3 Point numbers after insert ing points by FLAP lines with NUPU 2 and 3 Figure 11 NACA 23015 airfoil with and without variable geometry modification 5 4 3 Modification of Individual Points If NUPA 4H 0 individual points are modified NUPE NUPI and NUPU are ignored Fi nj which is the point number the ordinate y c of which is changed by Fy F is the vertical component of the change perpendicular to the surface in percent chord Positive F gt denotes a change toward the exterior of the airfoil i e a bump negative Fy a change toward the interior i e a dip F3 F1 and so on allow six more points to be modified For example 5 OPTIONS FOR BOTH DESIGN AND ANALYSIS MODES 31 FLAP19_uuuu3u 01 37 7 01 which moves point number 3 toward the exterior of the airfoil by 0 01 percent chord and point number 37 toward the interior by the same amount The modified airfoil replaces the original one because NUPE 9 5 4 4 Moment Reference Points The ALFA line invokes Subroutine MOMENT which computes the pitching moment and hinge moment coefficients Cm and cp respectively for each angle of attack The reference point for Cm is normally the quarter chord point and for cp the leading edge The coefficients are stored so they are available for other e g boundary layer
110. tion for other options the following options can be specified S followed by the two digits ab sets the label height to a b mm P followed by a character string replaces the default text with the character string Thus xP suppresses the default text in the upper left corner PN resets the text to the default text D appends the date and time to the character string given after P Z followed by a character string appends the character string to the previously specified text Options P and D are in this case not valid i e the Z option cannot be specified in the same REMO line as the P or D options 2 2 3 ENDE Line This line terminates the run The input lines are listed after the computed results 3 Airfoil Design The design of an airfoil is initiated by the TRA1 and TRA2 lines It is suggested that these lines be saved at least for those airfoils that are considered final in some sense Airfoil designers soon collect many such sets and it is often helpful to insert comments in the TRA1 line and TRA2 lines Any text input three columns after the last F number is ignored unless it is preceded by C in which case it will be written in the headline of the first output of the airfoil design The C option can be specified in each TRA1 line and all the comments up to 48 characters are then combined 3 AIRFOIL DESIGN 5 and written in sequence As described in detail in references 1 and 3 the airf
111. tion of displacement separation and transition of the boundary layer the airfoil drag and the occurence and effect of laminar separation bubbles The prediction of boundary layer separation has not been changed since 1963 ref 4 Separation 6 BOUNDARY LAYER ANALYSIS 42 is predicted when Hz decreases to 1 51509 in a laminar boundary layer and when H32 decreases to 1 46 in a turbulent boundary layer A displacement iteration was developed in 1980 ref 2 6 1 1 Criteria for Boundary Layer Transition In code versions since 1980 boundary layer transition was predicted by means of a local criterion In 1996 a new empirical transition criterion was implemented that considers the instability history of the laminar boundary layer which avoided the long computing time of the e method while achieving similar results in most cases Since then computing power has increased dramatically which has negated the disadvantage of the eN method Moreover the faster computers allowed a very large number of solutions of the Orr Sommerfield equation to be computed and tables to be constructed from which the amplification rates of the Tollmien Schlicting TS waves can be evaluated with adequate precision by interpola tion This increases the speed of the eN method such that the boundary layer computations require only 10 to 30 times more time than with the empirical criterion which is compensated by the higher computer speed The laminar boundary
112. to be computed E 12 n ke 12 where k is the so called k factor The default value 1 03 assumes a good planform The effect of wing twist is not considered The parasite drag area A parasite drag dynamic pressure is assumed to be constant and thus the aircraft parasite drag coefficient is Cp 13 where S is the wing area If the influence of various airfoils on the wing mass is to be evaluated for a given aircraft configuration the thicknesses of the airfoils must be considered The PLW line contains an option for this purpose that allows the wing planform to be alterred such that the absolute thickness of the different wings is the same To achieve this a reference thickness t c must be specified and if an airfoil having a thickness t c is to be evaluated the chords are multiplied by t t before any computations are performed A mass penalty due to the increased wing area that arises from the greater chords is also computed This procedure allows the influence of the airfoil on the overall aircraft performance to be evaluated in a more realistic manner than if the same planform were used for airfoils having different thicknesses Everything else is processed as it is for an FLZW line The a values in the preceding ALFA line are used Because the aircraft speed increases rapidly as the lift coefficient decreases more a values should be specified in the lower lift coefficient range The values of Umar p and v from the prec
113. uired in the code In the latter case which has only 44 input points the spacing of the points is not very suitable for the panel method It is recommended that the points omitted in reference 7 be splined back in This is accomplished by the following FXPR line See Chap 4 1 2 FXPRouuuu11851 841 831 821 811 61 151 41 31 21 FXPRuuuuu11761 17 51 41 1 31 21 6 1 51 41 3 1 21 Both lines insert the same points There is one more option available for Wortmann airfoils Although not recommended the thickness and the camber of Wortmann airfoils can be modified To accomplish this A is used as a factor THF If THF gt 0 the thickness distribution is multiplied by TH F without changing the mean line If THF lt 0 all y c values are multiplied by T HF Thus the y c values of the mean line are also modified 4 POTENTIAL FLOW AIRFOIL ANALYSIS 18 For example FXPRiuuuu31 FX 63 126 04 9235 These two lines invoke the first smoothing routine see Chap 4 1 1 and multiply all the y c values by 0 9235 Input of z c and y c for All Points If NUPU 2 the z c and y c values for all points must be specified NQ is ignored The number of points is determined from the input coordinates If A 0 all the z c and y c values are divided by the larger of X 1 and X NQ i e the more aft trailing edge point This normalization of the coordinates is not necessary if the x and y values are already in the
114. uring the development of the laminar boundary layer the frequency of the most amplified TS wave varies considerably Some of the TS waves that are initially amplified may be damped later whereas others may be amplified Sometimes the frequency of the most amplified TS wave is outside the defined frequency range The boundary layer computation is then halted and restarted at the first instability using an expanded frequency range Two typical examples of amplifications for many frequencies are shown in figure 17 The amplifications are plotted using dashed lines where the length of the dash is proportional to the frequency Thus higher frequencies are represented by shorter dashes and lower frequencies by longer dashes This gives a qualitative impression of the length of the TS waves The ordinate is the airfoil point number The amplifications are plotted only for these points although they are usually computed at many intermediate points as well The examples in figure 17 show that higher frequencies are often damped out after initially being amplified whereas lower frequencies are amplified later and finally reach the transition value 6 BOUNDARY LAYER ANALYSIS 43 10R 80 5 lower S 10R 320 9 upper S Airfoil 99 Z Airfoil 99 Ss PA Vat Ying UUA IN 7 WKS u e bap ry x ESS Z eS ZN A SS DAD SS os 2 gt Figure 17 Examples of amplification diagrams This method seems straightforwar
115. uters have become available Thus it was possible to develop a fast method for predicting transition by means of the e method and to improve the prediction of additional drag due to laminar separation bubbles The development of the code has been done in such a way that previous input data sets can still be used The results may however differ from those produced by earlier versions of the code Minor differences come from improvements to the panel method Larger differences result from the new transition method and the bubble drag which are now included in the normal natural transition mode The previous transition criteria are no longer available The latest version of the code along with the latest version of the user s guide is available for North America from for all other countries from Mr Dan M Somers Prof Dr Richard Eppler 122 Rose Drive Leibnizstr 84 Port Matilda PA 16870 7535 D 70193 Stuttgart USA Germany thank Mr Dan Somers for many suggestions and Drs Thorsten Lutz and Martin Hepperle for their assistance Stuttgart October 2005 Richard Eppler CONTENTS Contents 1 Principles of Code 1 1 1 2 1 3 Format f Inp t ines s dat ail a e e a AA A Se eas ee Character Strings for Supplementing Plots ooa a Date and E AAA 2 Overview of Input and General Options 2 1 2 2 Overview of Input Lines tipa Ad a General Options s iede Dieta Da birra 8 Grane amp S 2 OS Ol SSS i DIN AS Fen eB hn
116. w drag lift coefficient range 6 BOUNDARY LAYER ANALYSIS 64 REMO11 000 3 3 P ITEST E 387 TRAL 387 14 5 11 5 16 5 6 18 5 5 20 5 5 2 22 5 5 5 24 5 5 9 TRAL 387 26 5 6 5 28 5 7 3 30 5 8 5 0 9 2 33 5 2 5 35 5 3 9 37 5 4 9 TRAL 387 39 5 5 6 41 5 6 15 43 5 6 5 60 6 7 TRA21 38750001400010002 ALFA20 14 11 5234567 89 10 11 11 5 12 RE 3 200 3 04 200 CDCL 1 1 811 253111440 1 71132 L 100 9 16 23 35 56 67 85 97 108 115 118 RE 200 000 D 10000 210 130 94 98 113 122 130 128 132 169 250 6 T IExp Delft E Thesfaugth example illustrates the insertion of experimental data where more than one MU R pair E 387 9 06 7 R 0 2x10 E postas 0 2x10 without b d ea 7 qa a Exp Delft 4 Cy 0 57 0 T T T T T T T T T 0 5 10 208 Figure 21 Diagram for E 387 airfoil including experimental data is specified fig 22 The experimental data are fictitious The key is shifted upward by Ac 0 2 because it would otherwise have interfered with the curves REMO1 P 1iTest Exp Data TRA1 8 27 5 10 29 5 11 0 12 60 4 TRA26 8 4 17 5 2 1 7 4 17 5 2 1 7 600 ALFA20 1123 46 8 10 11 12 13 14 15 RE 3 2000 3 6000 CDCL 1 1 5211211240 2 253263 L 100 20 30 70 100 130 140 D 10000 100 75 80 85 95 200 12 T 1Exp Re 203M100H60J A 10 40 30 10 45 70 90 4 L 100 10 30 70 100 125 150 D 10000 100 60 62 65 105 160 6 xT 1Exp Re 603M100H60J E The final example plots a diagram containing only experimental
117. ween these two tables one line per iteration is written containing the values of Ks and Aa or AK for that iteration Other print modes are specified by mpr in the ABSZ line Chap 3 4 For example the TRA2 line for airfoil 1098 is TRA2 10984114 5 2 1 0 65 4 14 5020410 6506 400 3 AIRFOIL DESIGN 9 The listing produced by this TRA2 line and the previous TRA1 line see Chap 3 1 assuming the default print mode i e mpr 1 see ABSZ Line Chap 3 4 is given below The values of K and K are changed by the iteration The final values listed in the second table are underlined twice The other values influenced by the changes in K and K are underlined once The underlining has been added for clarity and is not produced by the code EPPLER CODE PROFIL98 V 16 6 98 RUN 17 6 98 10 28 TRANSCENDENTAL EQUATION RESULTS AIRFOIL 1098 ITERATION O MODE 6 NU ALPHA OMEGAP OMEGA K MU K H LAMBDA LAMBDA 23 8000 8 00 1 137 0 650 0 598 1 000 0 583060 14 50 4 00 27 8000 10 00 32 0050 12 00 60 0000 2 00 1 137 0 650 0 598 1 000 0 066661 14 50 4 00 ITERATION 1 KS 0 360403 DELTA 0 07527818 ROUNDED 0 075000 ITERATION 2 KS 0 392433 DELTA 0 00075381 ROUNDED 0 001000 ITERATION 3 KS 0 402662 DELTA 0 00026028 ROUNDED 0 000000 TRANSCENDENTAL EQUATION RESULTS AIRFOIL 1098 ITERATION 3 MODE 6 NU ALPHA OMEGAP OMEGA K MU K H LAMBDA LAMBDA 23 8000 8 00 1 182 0 641 0 622 1 000 0 459530 14 50 4 00 27 8000 10 00 32 0050
118. x data points are plotted as cy versus a also using symbol 5 The cy value of 1 1 is used in this plot 6 7 4 Line Types The line types 7 are defined by lengths 4 in mm of the lines and the spaces Line type 7 1 is a solid line For j gt 1 the line type is specified by m numbers from the array 12 floating point numbers beginning with n The first length 4 where i n is drawn the next length 1 is not drawn i e a space and so on After the last 4 where i nj m 1 the cycle is repeated starting with the first 4 The variable m must be divisible by 2 and less than 9 The variables m and n are stored in arrays containing five integers each The default values for 7 2 3 4 5 6 andi 1 2 12 are mj 2 4 6 8 2 nj 1 3 3 3 5 fi 5 2 10 2 2 2 2 2 22 which specify the following line types the line segments are underlined the space segments are not J j 2 5mm 2mm j 3 10mm 2mm 2mm 2mm j 4 10mm 2mm 2mm 2mm 2mm 2mm a 10mm 2mm 2mm 2mm 2mm 2mm 2mm 2mm as ee eee ee eee 2mm 2mm If NUPA 0 and F gt 0 new values for mj and n are specified In this case the five digits of F specify n2 Ng the five digits of Fy ma mg and F3 F 4 the 4 For example CDCL 1 Lu 1553_ 24422 5 2 5 2 10 2 2 2 which specifies the following line types
119. xplanation blocks can be placed within the diagram If Wz 2 W745 are not zero they specify the coordinates of the upper left corners of the explanation blocks Wz 2 and W 3 position the block that explains the bubble warnings Wz 4 and Wz 5 the block that defines the abbreviations Wz and W 4 specify the horizontal positions Wr 3 and Wz15 the vertical positions The positions of both blocks must be specified if the default position of either is changed The N and Z options are exercised as described under DIAG Line Chap 5 6 After i where i 1 2 7 additional text can be given that will be inserted between the th line type and its explanation Here 7 may be greater than the total number of line types in which case additional text lines are plotted below the line types and their explanations This option is primarily useful in conjunction with LAUF 4H 0 or when experimental results are included Here also an F at the end of the string plots the current flap data and iF adds only the flap data to the labels After the flap data the labels R or c are plotted to clarify the succeeding numbers The options may require more than one input line An F can be inserted in the DLFF words which continues the input on the next line Moreover in the first line that contains an option can be given and then a second line containing further options can be given 6 7 3 Experimental Data Experimental
120. y flap such as a Flettner flap or to introduce a flap on an airfoil after having modified its shape using the variable geometry option If another FLAP line is inserted after a FLAP line with NUPE lt 8 a new modification of the old original airfoil will be initiated whereas inserting another FLAP line after a FLAP line with NUPE gt 8 will cause the shape as resulting from the first FLAP line to be modified If NUPE 9 the thickness of the modified airfoil relative to its chord is evaluated The new thickness replaces the thickness of the original airfoil For example the deflection of a simple flap changes the relative thickness because the airfoil chord changes If NUPE 8 the evaluation of the new thickness is not performed and the thickness remains unchanged This is common practice in the case of simple flaps The panel method is invoked automatically after a FLAP line with NUPU 0 4 or 5 or NUPA 0 Note that the number of points may be increased by FLAP lines The maximum number of points on the original airfoil must be no more than 121 The panel method can accommodate up to 129 points The modification of an airfoil with 121 points by a FLAP line with NUPU 0 i e a simple flap is therefore possible The variable geometry option is also allowed to increase the number of points up to 129 A modification that yields more than 129 points however causes the code to stop 5 4 1 Simple Flap If NUPU 0 the airfoil sh
121. yer separation NACA 23012 12 U upper surface 7 L lower surface fbR 10 TEE bR 2 5x10 yi 25 Flap 10 R 10 aaeei 25 Flap 10 R 2 5x10 1 5 Co 1 0 57 0 gt 5 Figure 19 Diagram for unflapped and flapped NACA 23012 airfoil airfoil In this case it would have been simpler to evaluate the more highly cambered SU2 airfoil first then no extension of the frame would have been necessary The airfoil name is changed to include both airfoil names The thickness of the second airfoil 15 87 is plotted after the thickness of the first airfoil using the Z option The line explanations are supplemented by the corresponding airfoil names For each airfoil three boundary layer calculations are performed for one Reynolds number R 600 000 one with MU 3 one with MU 3 04 and one with MU 3 02 The drag is thus computed once including the bubble drag from both surfaces once including no bubble drag and once includ ing bubble drag from only the upper surface which is denoted in the corresponding line explanation by an additional u The difference between the polar curve exhibiting the lowest drag and the middle curve is therefore the bubble drag from the upper surface The difference between the middle curve and the curve exhibiting the highest drag is the bubble drag from the lower surface At high lift coefficients the second airfoil exhibits bubble drag only from the upper surface Thus t

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