XFoil question
Keta
Reynolds number of approximately 1e6. I want to test it first with
XFoil, but what is the Reynolds number I have to use, in order to know
the coefficient of lift I'll get in the wind tunnel test? In XFoil,
the chord is set to unity; should I use the same Reynolds number or do
I have to scale it?
At first, I thought the same Re should be used, but after reading the
documentation I got confused. I'm a little messed up, I need your help.
Praveen C
Reynolds number is a non-dimensional quantity. You must compute at the
same Re as your wind tunnel test.
Keta
definition of Re number, not taking into account any characteristic
length. Here is what the documentation says about units:
======================================
Units
=====
Most XFOIL operations are performed on the airfoil's cartesian
coordinates x,y , which do not necessarily have a unit chord c.
Since the chord is ambiguous for odd shapes, the XFOIL
force coefficients CL, CD, CM are obtained by normalizing the
forces and moment with only the freestream dynamic pressure
(the reference chord is assumed to be unity). Likewise, the
XFOIL Reynolds number RE is defined with the freestream velocity
and viscosity, and an implied unit chord:
CL = L / q | V = freestream speed
CD = D / q | v = freestream kinematic viscosity
CM = M / q | r = freestream density
RE = V / v | q = 0.5 r V^2
The conventional definitions are
Cl = L / q c
Cd = D / q c
Cm = M / q c^2
Rc = V c / v
so that the conventional and XFOIL definitions differ only by
the chord factor c or c^2.
For example, a NACA 4412 airfoil is operated in the OPER menu at
RE = 500000
ALFA = 3
first with chord=1.0, and then with chord=0.5 (changed with SCAL
command in the GDES menu, say). The results produced by XFOIL are:
c = 1.0 : CL = 0.80 CD = 0.0082 (RE = 500000, Rc = 500000)
c = 0.5 : CL = 0.40 CD = 0.0053 (RE = 500000, Rc = 250000)
Since CL is not normalized with the chord, it is nearly proportional
to the airfoil size. It is not exactly proportional, since the true
chord Reynolds number Rc is different, and there is always a weak
Reynolds number effect on lift. In contrast, the CD for the smaller
airfoil is significantly greater than 1/2 times the larger-airfoil
CD,
since chord Reynolds number has a significant impact on profile
drag.
Repeating the c = 0.5 case at RE = 1000000, produces the expected
result that CL and CD are exactly 1/2 times their c = 1.0 values.
c = 0.5 : CL = 0.40 CD = 0.0041 (RE = 1000000, Rc = 500000)
Although XFOIL performs its operations with no regard to the size
of the airfoil, some quantities are nevertheless defined in terms
of the chord length. Examples are the camber line shape and BL trip
locations, which are specified in terms of the relative x/c,y/c along
and normal to the airfoil chord line. This is done only for the
user's
convenience. In the input and output labeling, "x,y" always refer
to the cartesian coordinates, while "x/c,y/c" refer to the chord-
based coordinates which are shifted, rotated, and scaled so that
the airfoil's leading edge is at (x/c,y/c) = (0,0), and
the airfoil's trailing edge is at (x/c,y/c) = (1,0). The two
systems cooincide only if the airfoil is normalized.
======================================
Note that the usual Re is written as Rc. Now I think that I have to
scale the Reynolds number, and perform the calculations with RE=Rc/c,
and then I'll get Cl as Cl=CL/c, but I'm not sure.
Praveen C
prepare the airfoil geometry with unit chord. Then the Cl you get should
be comparable with wind tunnel value (I dont know if you simulate the
wind tunnel walls in xfoil, that can have some effect)