Axisymmetry problem and XFOIL
 

Dear All I would like to get the boundary layer evolution around a rotationally symmetrical body (kind of fuselage). The problem is axisymmetric, so that I can plot the shape of the fuselage in a 2d plan. However, does XFOIL is able to give an answer for this problem? The equation used by the code are still valid for axisymmetric shapes? Thanks

Xfoil hack for drag of axisymmetric bodies of revolution
 

Here's how I did this. First, you need a version of Xfoil compiled from source. That's because you're going to change the code and recompile it. I'm also assuming you've got a Linux system, where make commands work. In Windows, you're on your own for compiling. And finally, of course, I'm assuming that the airfoil you loaded is symmetrical.

Assuming you've got that, navigate to the Xfoi/src directory.

1. In xfoil.f, find the line (about line 1178 in my version, 6.97) that computes CD. It reads like this:

CD = 2.0*THWAKE * (UEWAKE/QINF)**(0.5*(5.0+SHWAKE))

After that line (and before the ELSE) insert the following lines:

C
C------ compute axisymmetric drag coeff CDX for body of revolution in a
C similar manner, using frontal area FRS as reference area.
C First term is now area of wake as defined by theta.
FRS = PI*(THICKB*0.5)**2
CDX = 2.0*PI*THWAKE**2 * (UEWAKE/QINF)**(0.5*(5.0+SHWAKE)) / FRS


Theta is the boundary layer momentum thickness and THWAKE is theta in the downstream wake. For axisymmetric flow, instead of multiplying by 2 (which you do in 2-d to get total thickness of the wake) we use the area of circle to get the AREA of the wake, and convert to Cd by dividing by the cross sectional area FRS. The other terms of the equation are for the wake momentum and don't change. Easy, no? [Reference: J.L. Hess & R.M. James, "On the problem of shaping an axisymmetric body to obtain low drag at large Reynolds numbers," McDonnel Douglas report MDC J6791, (1975).]

2. In XFOIL.INC define the two new variables you just used. You can really do this
anywhere as long as you define them as real. To be consistent, I did this in the same
line where CD is defined (just added CDX and FRS to the line), like this:

COMMON/CR09/ ADEG,ALFA,AWAKE,MVISC,AVISC,
& XCMREF,YCMREF,
& CL,CM,CD,CDP,CDF,CL_ALF,CL_MSQ,CDX,FRS,
& PSIO,CIRC,COSA,SINA,QINF,
& GAMMA,GAMM1,
& MINF1,MINF,MINF_CL,TKLAM,TKL_MSQ,CPSTAR,QSTAR,
& CPMN,CPMNI,CPMNV,XCPMNI,XCPMNV

3. In xoper.f, output your result. Find the line where results are written to the screen (not the plot) which is about line 2704 in my version. It looks line this:

WRITE(*,2020) ALFA/DTOR, CL, CM, CD, CDF, CDP

Below this, add the line:

WRITE(*,2025) CDX

Then add the format line you just referenced. I put it just below line label 2020, though it really can go anywhere in subroutine VISCAL

2025 FORMAT ('Axisymmetric drag CDx =',F9.7 )

Finally, save all files and compile. In directory /Xfoil/bin issue a "make xfoil" to compile it all up.

KAP

Could you explain why the momentum thikness does not change?
Indeed, for an inviscid solution surface velocities on 2d airfoil and axisymmetric body with the same profile will be quite different, so bl equations too.

Is this explained in the reference given above?

Truffaldino