Mixed-Inverse Design Routine (QDES)

Table of contents

1. Creation of seed surface speed distribution
2. Modification of surface speed distribution
3. Generation of new airfoil geometry

XFOIL’s Mixed-Inverse facility (QDES) is useful in certain redesign problems where parts of the airfoil cannot be altered under any circumstances. The Mixed-Inverse menu is shown below.

   <cr>   Return to Top Level

   QSET   Reset Qspec <== Q

   Modi   Modify Qspec
   MARK   Mark off target segment
   SMOO   Smooth Qspec inside target segment
   SLOP   Toggle modified-Qspec slope matching flag

   eXec i Execute mixed-inverse calculation
   REST   Restore geometry from buffer airfoil
   CPXX   CPxx endpoint constraint toggle

   Plot   Plot Qspec (line) and Q (symbols)
   VISC   Qvis overlay toggle
   REFL   Reflected Qspec overlay toggle

   Blow   Blowup plot region
   Rese   Reset plot scale and origin
   Wind   Plot window adjust via cursor and keys

   SIZE r Change absolute plot-object size
  .ANNO   Annotate plot
   HARD   Hardcopy current plot

The QDES menu above is intentionally geared for the redesign of a segment of an existing airfoil (with its surface speed distribution calculated previously in OPER) rather than the generation of a totally new airfoil.

Creation of seed surface speed distribution

When QDES is entered, the specified speed distribution Qspec is initialized to the current speed distribution Q last set in OPER. If a direct solution for the current airfoil hasn’t been calculated yet, QDES goes ahead and calculates it, using the last-set angle of attack. If this isn’t the desired angle, it can be set in OPER using ALFA. QSET can then be used to set Qspec from the current Q distribution. The QSET command can be used anytime later to “reset” Qspec if the modification has been botched.

Modification of surface speed distribution

Qspec can be repeatedly modified with the screen cursor and the MODI command, exactly as in MDES. It is also necessary to mark off the target segment where the geometry is to be modified with the MARK command.

Generation of new airfoil geometry

EXEC modifies the airfoil over the target segment to match Qspec there as closely as possible. The remainder of the airfoil geometry is left unaltered. EXEC requests the number of Newton iterations to be performed in the inverse calculation. Although as many as six iterations may be required for convergence to machine zero, it is not necessary to fully converge a Mixed-Inverse case. Two iterations are usually sufficient to get very close to the new geometry. In any case, the new surface speed distribution Q which actually results from the inverse calculation will typically differ somewhat from the specified distribution Qspec by function modes which are added to Qspec. At least two modes are added, with their magnitudes determined by geometric closure requirements at the inverse segment endpoints. As with the MDES complex-mapping routine, the necessary modifications to Qspec will be smallest if Qspec is modified so that CL (the area under the Qspec(s) curve) is roughly preserved.

Issuing PLOT after the EXEC command finishes will compare the specified (Qspec) and resulting (Q) speed distributions. If extra smoothness in the surface speed is required, the CPXX command just before EXEC will enable the addition of two additional modes which allow the second derivative in the pressure at the endpoints to be unchanged from the starting airfoil. The disadvantage of this option is that the resulting surface speed Q will now deviate more from the specified speed Qspec. It is allowable to repeatedly modify Qspec, set or reset the CPXX option, and issue the EXEC command in any order.

The Mixed-Inverse modification is performed on the current airfoil directly, in contrast to Full-Inverse which generates the buffer airfoil as its output. In fact, it is important not to issue the PANE or PCOP commands at top level after doing work in the QDES menu, as the new current airfoil will be overwritten with the old buffer airfoil.