.: code PanelM_2D

calculates by panel method the integral parameters and pressure distribution on multi-element airfoil.
The user interface is implemented using FOX toolkit library.

Input data (the general data for configuration):

  1. FIOG = 0 - 6 - parameter defines the level of details of output calculation results.
  2. FNFOIL the number of elements of configuration.
  3. COND_GUK the length of additional panel if Zukowsky-Kutta condition is realised using the additional panel.
  4. N_CORR compressibility correction.
    N_CORR=1 - correction of Prandtl-Glauret .
    N_CORR=2 - correction of Karman-Tsien.
    N_CORR=3 - correction of Laitone.
  5. N_Cond - the method of realisation of a condition Zhukowsky-Kutta .
    N_Cond =1 - the additional panel and control point.
    N_Cond =2 - equality of Cp in control points of the upper and lower panels on a trailing edge.
  6. ME_GEOM = 1 - the relative positioning of elements is defined by input geometry of each element.
    ME_GEOM = 2 - the relative positioning of elements is defined by parameters XAX,YAX,XX,YY,DFL.
  7. I_BL = 1 - boundary layer calculation.
    I_BL = 0 - no boundary layer calculation.
  1. ALPHA - angle of attack.
  2. MACH - Mach number.
  3. SWEPT - angle of swept of the infinite swept wing. Here, the geometry of infinite swept wing is specified by airfoil in normal direction to the leading edge.
  4. B_REF - the reference length.
  5. X_MZ0 X-coordinate for calculating the moment coefficient of the configuration.
  6. Y_MZ0 Y-coordinate for calculating the moment coefficient of the configuration.

next 5 parameters should be if I_BL = 1:

  1. RE mill - Reynolds number (Re_mill = 1.0 equal Re=1000000).
  2. ETAE - the initial value of trasformed boundary layer thickness (usually: 6-8).
  3. NP0_BL - the initial number steps Hj for boundary layer calculation (usually: 21-41).
  4. V_BL - Hj+1/Hj (usually: 1.1-1.3).
  5. CF_SEP = Cf*sqrt(Re), the boundary layer after separation is calculated by inverse method with specified friction coefficient ( CF_SEP=0.1 corresponds Cf=0.1/sqrt(Re)).

Input data (for each element):

  1. B0 - the reference length of the element.
  2. FNF - method of specifying the input geometry of an element.
    FNF=1 -from the leading edge to the trailing edge along the upper and lower surfaces FNF=2 -from the trailing edge along the upper surface to the leading edge, along the lower surface to the trailing edge. FNF=3 -from the trailing edge along the lower surface to the leading edge, along the upper surface to the trailing edge.
  3. FNP - the number of nodes of the input geometry
  4. FNM - the number of panels on the element (even, <590, summa of the panels of the multi-element configuration <1180)
  5. FNROT - to align the element chord with the X axis or not?
    FNROT=0 - no align. FNROT=1 - to align.
  6. FNSM - Parameter of smoothing
    FNSM=0 - no smoothing. FNSM=1 - smoothing.
  7. FNLE - the sequence number of the leading edge node in input geometry of the element
  8. SCALE - the scale of the input geometry of the element.
  1. XAX X-coordinate of the rotation axis in the coordinate system of the element.
  2. YAX Y-coordinate of the rotation axis in the coordinate system of the element.
  3. XX X-coordinate of the rotation axis in the coordinate system of the main (the first in the input file) element.
  4. YY Y-coordinate of the rotation axis in the coordinate system of the main (the first in the input file) element.
  5. DFL - the angle of deflection of the element.
  6. X_MZ X-coordinate for calculating the moment of the element.
  7. Y_MZ Y-coordinate for calculating the moment of the element.

The input file FN.dat have to contain these data.

.: Panel: Multi Element Airfoil Calculation

This panel contains the graphic window with the view of the multielemeht aerofoil and the pressure distribution on each element.
Each time the [SAVE RESULT] button is pressed, a new file InputFile_i.sum, (i-sequence number) is created with the current calculation result .

.: general input data:

Alpha angle of attack
Mach Mach number
Swept angle of swept of the infinite swept wing.
B ref the reference length

.: calculation results:

Clift total lift coefficientи
Cdrag total drag coefficient
Cmz total moment coefficient
Clift(g) total lift coefficient (summa gamma)

.: compressibility correction:

No no correction
Prandtl-Glauret Prandtl-Glauret correction
Karman-Tsien Karman-Tsien correction
Laitone Laitone correction

.: Zhukowsky-Kutta condition:

Add.Point additional panel and control point
Cp EQ equality of Cp in the control points of the upper and lower panels at the trailing edge

.: Increment:

XY Increment for axis position
Angle Increment for angle position

.: Parameters for each elements:

main:
B elem the reference length of element
Npanels number of panels on the element
Axis position:
Xf X-coordinate of the rotation axis in the coordinate system of the element.
Yf Y-coordinate of the rotation axis in the coordinate system of the element.
Xc X-coordinate of the rotation axis in the coordinate system of the main (the first in the input file) element.
Yc Y-coordinate of the rotation axis in the coordinate system of the main (the first in the input file) element
Angle angle of deflection of the element
integral calculation results:
Clift the lift coefficient of the element related to reference length of element
Cdrag the drag coefficient of the element related to reference length of element
Cmz the momentum coefficient of the element related to reference length of element
Clift(g) the lift coefficient of the element (summa gamma)
Clift*b the lift coefficient of the element
Cmzo coefficient of the element's moment relative to the leading edge of the main (the first in the input file) element

If you press the button [BL Calculation] on the panel Multi Element Airfoil Calculation the boundary layer is calculated on the upper and lower surfaces of each element.
Then you will see the panel BL calculation. Multielement aerofoil .

.: Panel: BL calculation. Multielement aerofoil

This panel contains two graphic windows.
The upper window contains the plot of the pressure distribution on the upper or lower surface of the the chosen element. The spin control [N elem] defines chosen element.
The lower window contains the plot of one of the boundary layer parameters.

The coordinates of the transition point (from stagnation point):
Xtru for the upper surface.
Xtrl for the lower surface.

.: Comparison with analytical solution from paper:
B. R. WILLIAMS," An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils".

Configuration A. The main airfoil - 80 panels, flap - 48 panels.

Configuration B. The main airfoil - 60 panels, flap - 40 panels.

.: The example of input file for 2-element airfoil of Williams, Configuration A:

FIOG FNFOIL COND_GUK N_CORR N_Cond ME_GEOM
5.0 2.0 0.0003 0.0 0.0 1.
AP MACH SWEPT B_REF X_MZ0 Y_MZ0
0.0 0.0 0. 1.0 0.0 0.0
B0 FNF FNP FNM FNROT FNSM FNLE SCALE
1.0 3.0 61.0 80.0 0.0 0.0 31. 1.
XAX YAX XX YY DFL X_MZ Y_MZ
0.0 0.0 0.0 0.0 0. 0.0 0.0
X Y d
0.99931 0.00612 0.00
0.99417 0.00748 0.001
0.98434 0.00903 0.001
0.96975 0.00941 0.001
0.94998 0.00766 0.001
0.92461 0.00361 0.001
0.89358 -0.00236 0.001
0.85728 -0.00965 0.001
0.81639 -0.01771 0.001
0.77169 -0.02612 0.001
0.72396 -0.03451 0.001
0.67396 -0.04261 0.001
0.62240 -0.05018 0.001
0.56993 -0.05699 0.001
0.51716 -0.06287 0.001
0.46466 -0.06766 0.001
0.41297 -0.07114 0.001
0.36259 -0.07350 0.001
0.31398 -0.07438 0.001
0.26759 -0.07386 0.001
0.22381 -0.07194 0.001
0.18304 -0.06866 0.001
0.14563 -0.06409 0.001
0.11190 -0.05833 0.001
0.08214 -0.05151 0.001
0.05663 -0.04378 0.001
0.03560 -0.03530 0.001
0.01927 -0.02625 0.001
0.00783 -0.01681 0.001
0.00143 -0.00714 0.001
0.00017 -0.0008 0.001
0.00409 0.01242 0.001
0.01311 0.02211 0.001
0.02707 0.03155 0.001
0.04582 0.04056 0.001
0.06914 0.04898 0.001
0.09681 0.05663 0.001
0.12857 0.06335 0.001
0.16414 0.06902 0.001
0.20321 0.07352 0.001
0.24543 0.07678 0.001
0.29044 0.07875 0.001
0.33785 0.07942 0.001
0.38724 0.07881 0.001
0.43814 0.07700 0.001
0.49010 0.07408 0.001
0.54258 0.07019 0.001
0.59507 0.06550 0.001
0.64697 0.06020 0.001
0.69769 0.05453 0.001
0.74656 0.04870 0.001
0.79290 0.04293 0.001
0.83597 0.03743 0.001
0.87501 0.03232 0.001
0.90929 0.02762 0.001
0.93815 0.02323 0.001
0.96122 0.01893 0.001
0.97850 0.01458 0.001
0.99043 0.01041 0.001
0.99753 0.00718 0.001
1.00000 0.00590 0.000
B0 FNF FNP FNM FNROT FNSM FNLE SCALE
1.0 3.0 61.0 48.0 0.0 0.0 24. 1.
XAX YAX XX YY DFL X_MZ Y_MZ
0.0 -0.00 0.0 -0.00 0. 0.0 0.0
X Y d
1.31360 -0.20335 0.00
1.31121 -0.20083 0.001
1.30635 -0.19598 0.001
1.29886 -0.18893 0.001
1.28864 -0.17996 0.001
1.27564 -0.16939 0.001
1.25995 -0.15765 0.001
1.24177 -0.14518 0.001
1.22146 -0.13243 0.001
1.19948 -0.11982 0.001
1.17640 -0.10766 0.001
1.15285 -0.09619 0.001
1.12944 -0.08553 0.001
1.10676 -0.07572 0.001
1.08535 -0.06674 0.001
1.06565 -0.05854 0.001
1.04799 -0.05105 0.001
1.03263 -0.04423 0.001
1.01972 -0.03807 0.001
1.00930 -0.03258 0.001
1.00134 -0.02781 0.001
0.99572 -0.02381 0.001
0.99226 -0.02065 0.001
0.99073 -0.01835 0.001
0.99087 -0.01686 0.001
0.99242 -0.01604 0.001
0.99508 -0.01571 0.001
0.99864 -0.01569 0.001
1.00295 -0.01582 0.001
1.00797 -0.01598 0.001
1.01372 -0.01607 0.001
1.02027 -0.01609 0.001
1.02768 -0.01606 0.001
1.03600 -0.01610 0.001
1.04527 -0.01631 0.001
1.05548 -0.01684 0.001
1.06658 -0.01785 0.001
1.07852 -0.01946 0.001
1.09119 -0.02181 0.001
1.10447 -0.02499 0.001
1.11824 -0.02909 0.001
1.13235 -0.03415 0.001
1.14667 -0.04020 0.001
1.16103 -0.04725 0.001
1.17532 -0.05525 0.001
1.18938 -0.06416 0.001
1.20310 -0.07391 0.001
1.21637 -0.08439 0.001
1.22907 -0.09548 0.001
1.24112 -0.10704 0.001
1.25245 -0.11891 0.001
1.26298 -0.13090 0.001
1.27267 -0.14281 0.001
1.28147 -0.15440 0.001
1.28934 -0.16544 0.001
1.29624 -0.17566 0.001
1.30214 -0.18476 0.001
1.30697 -0.19245 0.001
1.31064 -0.19840 0.001
1.31303 -0.20226 0.001
1.31365 -0.20325 0.0

.: The example of input file for Joukowski airfoil with the boundary layer calculation:

FIOG FNFOIL COND_GUK N_CORR N_Cond ME_GEOM I_BL
4.0 1.0 0.001 0.0 0.0 0. 1.
AP MACH SWEPT B_REF X_MZ0 Y_MZ0
2.0 0.0 0. 1.0 0.0 0.0
Re mill ETAE NPO BL V BL Cf sep
1.0 6.0 21. 1.2 -0.1
B0 FNF FNP FNM FNROT FNSM FNLE SCALE
1.0 2.0 81.0 128.0 0.0 0.0 41. 1.
XAX YAX XX YY DFL X_MZ Y_MZ X_TRU X_TRL
0.0 0.0 0.0 0.0 0. 0.0 0.0 0.03 0.03
X Y d
1.000000 0.000000 0.00
0.998516 0.000013 0.001
0.994074 0.000106 0.001
0.986700 0.000355 0.001
0.976442 0.000834 0.001
0.963363 0.001606 0.001
0.947543 0.002731 0.001
0.929079 0.004252 0.001
0.908085 0.006205 0.001
0.884686 0.008609 0.001
0.859023 0.011472 0.001
0.831248 0.014783 0.001
0.801526 0.018520 0.001
0.770030 0.022643 0.001
0.736943 0.027101 0.001
0.702456 0.031825 0.001
0.666767 0.036740 0.001
0.630079 0.041756 0.001
0.592604 0.046776 0.001
0.554554 0.051697 0.001
0.516147 0.056412 0.001
0.477603 0.060813 0.001
0.439147 0.064792 0.001
0.401001 0.068246 0.001
0.363391 0.071078 0.001
0.326540 0.073198 0.001
0.290670 0.074530 0.001
0.256001 0.075008 0.001
0.222748 0.074584 0.001
0.191120 0.073223 0.001
0.161320 0.070910 0.001
0.133542 0.067647 0.001
0.107968 0.063455 0.001
0.084771 0.058371 0.001
0.064106 0.052452 0.001
0.046117 0.045773 0.001
0.030928 0.038420 0.001
0.018646 0.030497 0.001
0.009356 0.022118 0.001
0.003126 0.013406 0.001
0.000000 0.000000 0.001
0.003126 -0.013406 0.001
0.009356 -0.022118 0.001
0.018646 -0.030497 0.001
0.030928 -0.038420 0.001
0.046117 -0.045773 0.001
0.064106 -0.052452 0.001
0.084771 -0.058371 0.001
0.107968 -0.063455 0.001
0.133542 -0.067647 0.001
0.161320 -0.070910 0.001
0.191120 -0.073223 0.001
0.222748 -0.074584 0.001
0.256001 -0.075008 0.001
0.290670 -0.074530 0.001
0.326540 -0.073198 0.001
0.363391 -0.071078 0.001
0.401001 -0.068246 0.001
0.439147 -0.064792 0.001
0.477603 -0.060813 0.001
0.516147 -0.056412 0.000
0.554554 -0.051697 0.001
0.592604 -0.046776 0.001
0.630079 -0.041756 0.001
0.666767 -0.036740 0.001
0.702456 -0.031825 0.001
0.736943 -0.027101 0.001
0.770030 -0.022643 0.001
0.801526 -0.018520 0.001
0.831248 -0.014783 0.001
0.859023 -0.011472 0.001
0.884686 -0.008609 0.001
0.908085 -0.006205 0.001
0.929079 -0.004252 0.001
0.947543 -0.002731 0.001
0.963363 -0.001606 0.001
0.976442 -0.000834 0.001
0.986700 -0.000355 0.001
0.994074 -0.000106 0.001
0.998516 -0.000013 0.001
1.000000 0.000000 0.000