Analysis
Most of the commands in the top level XFOIL menu merely put the user into some lower command level with its own menu and prompt. Issuing The OPER command, for instance, will produce the prompt
.OPERi c>
Typing a “ ? “ will result in the OPER analysis menu being displayed:
<cr> Return to Top Level
! Redo last ALFA,CLI,CL,ASEQ,CSEQ,VELS
Visc r Toggle Inviscid/Viscous mode
.VPAR Change BL parameter(s)
Re r Change Reynolds number
Mach r Change Mach number
Type i Change type of Mach,Re variation with CL
ITER Change viscous-solution iteration limit
INIT Toggle BL initialization flag
Alfa r Prescribe alpha
CLI r Prescribe inviscid CL
Cl r Prescribe CL
ASeq rrr Prescribe a sequence of alphas
CSeq rrr Prescribe a sequence of CLs
SEQP Toggle polar/Cp(x) sequence plot display
CINC Toggle minimum Cp inclusion in polar
HINC Toggle hinge moment inclusion in polar
Pacc i Toggle auto point accumulation to active polar
PGET f Read new polar from save file
PWRT i Write polar to save file
PSUM Show summary of stored polars
PLIS i List stored polar(s)
PDEL i Delete stored polar
PSOR i Sort stored polar
PPlo ii. Plot stored polar(s)
APlo ii. Plot stored airfoil(s) for each polar
ASET i Copy stored airfoil into current airfoil
PREM ir. Remove point(s) from stored polar
PNAM i Change airfoil name of stored polar
PPAX Change polar plot axis limits
RGET f Read new reference polar from file
RDEL i Delete stored reference polar
GRID Toggle Cp vs x grid overlay
CREF Toggle reference Cp data overlay
FREF Toggle reference CL,CD.. data display
CPx Plot Cp vs x
CPV Plot airfoil with pressure vectors (gee wiz)
.VPlo BL variable plots
.ANNO Annotate current plot
HARD Hardcopy current plot
SIZE r Change plot-object size
CPMI r Change minimum Cp axis annotation
BL i Plot boundary layer velocity profiles
BLC Plot boundary layer velocity profiles at cursor
BLWT r Change velocity profile scale weight
FMOM Calculate flap hinge moment and forces
FNEW rr Set new flap hinge point
VELS rr Calculate velocity components at a point
DUMP f Output Ue,Dstar,Theta,Cf vs s,x,y to file
CPWR f Output x vs Cp to file
CPMN Report minimum surface Cp
NAME s Specify new airfoil name
NINC Increment name version number
The commands are not case sensitive. Some commands expect multiple arguments, but if the arguments are not typed, prompts will be issued.
The most commonly-used commands have alternative short forms, indicated by the uppercase part of the command in the menu list. For example, the menu shows…
Alfa r Prescribe alpha
CLI r Prescribe inviscid CL
Cl r Prescribe CL
ASeq rrr Prescribe a sequence of alphas
CSeq rrr Prescribe a sequence of CLs
The “A” command is the short alternative form of “ALFA”, and “C” is the short alternative of “CL”. Likewise, “AS” and “CS” are the short forms of “ASEQ” and “CSEQ”. The CLI command has no short form (as indicated by all capitals in the menu), and must be fully typed.
Hopefully, most of the commands are self-explanatory. For inviscid cases, the CLI and CL commands are identical. For viscous cases, CLI is equivalent to specifying alpha, this being determined a priori from the specified lift coefficient via an inviscid solution. CL will return a viscous solution with the specified true viscous lift coefficient at an alpha which is determined as part of the solution (prescribing a CL above CLmax will cause serious problems, however!). The user is always prompted for any required input. When in doubt, typing a “ ? “ will always produce a menu.
After an ALFA, CL, or CLI command is executed, the Cp vs x distribution is displayed, and can be displayed again at any time with CPX. If the viscous mode is active, the true viscous Cp is shown as a solid line, and the inviscid Cp at that same alpha is shown as a dashed line. Each dash covers one panel, so the local dashed line density is also a useful visual indicator of panel resolution quality. If the inviscid mode is active, only the inviscid Cp is shown as a solid line.
The difference between the true viscous Cp distribution (solid line) and the inviscid Cp distribution (dashed line) is due to the modification of the effective airfoil shape by the boundary layers. This effective airfoil shape is shown superimposed on the actual current airfoil shape under the Cp vs x plot. The gap between these effective and actual shapes is equal to the local displacement thickness delta*, which can also be plotted in the VPAR menu.
This is only about 1/3 to 1/2 as large as the overall boundary layer thickness, which can be visualized via the BL or BLC commands which diplay velocity profiles through the boundary layer. BL displays a number of profiles equally spaced around the airfoil’s perimeter, while BLC displays profiles at cursor-selected locations. The zooming commands Z, U, may be necessary to better see these small profiles in most cases.
If the Cp reference data overlay option is enabled with CREF, initiating a Cp vs x plot will first result in the user being prompted for a formatted data file with the following format:
x(1) Cp(1)
x(2) Cp(2)
. .
. .
The Cp vs x plot is then displayed as usual but with the data overlaid. If FREF has been issued previously, then numerical reference values for CL, CD, etc. will be requested and added to the plot next to the computed values.
Boundary-layer quantities are plotted from the VPLO menu:
H Plot kinematic shape parameter
DT Plot top side Dstar and Theta
DB Plot bottom side Dstar and Theta
UE Plot edge velocity
CF Plot skin friction coefficient
CD Plot dissipation coefficient
N Plot amplification ratio
CT Plot max shear coefficient
RT Plot Re_theta
RTL Plot log(Re_theta)
X rrr Change x-axis limits
Y rrr Change y-axis limits on current plot
Blow Cursor blowup of current plot
Rese Reset to default x,y-axis limits
SIZE r Change absolute plot-object size
.ANNO Annotate plot
HARD Hardcopy current plot
GRID Toggle grid plotting
SYMB Toggle node-symbol plotting
LABE Toggle label plotting
CLIP Toggle line-plot clipping
This menu is largely self-explanatory. The skin friction coefficient plotted with the CF command is defined as
2
Cf = tau / 0.5 rho Qinf
This differs from the standard boundary layer theory definition which uses the local Ue rather than Qinf for the normalization. Using the constant freestream reference makes Cf(x) have the same shape as the physical shear stress tau(x).
The dissipation coefficient CD’ (this is NOT the drag coefficient!!!) is plotted with the CD command. CD’(x) is proportional to the local energy dissipation rate due to viscous shear and turbulent mixing. Hence, it indicates where on the airfoil drag is being created. It is in fact a much better indicator of drag production than Cf(x), since Cf does not account for pressure drag. CD’, on the other hand, accounts for everything. Its relationship to the total profile drag coefficient is simply
/ CD = | 2 CD' ds
/
with the integration performed over both boundary layers and also the wake. It will be seen that if the flow is separated at the trailing edge, much of the drag contribution (energy dissipation) of CD’ occurs in the wake.
As mentioned earlier, all forces are normalized with freestream dynamic pressure only. CL, CD, CM are the usual chord-based definitions only if the airfoil has a unit chord – in general, they will scale with the airfoil’s chord. Also, CM is defined about the cartesian point (xref,yref) = (0.25,0.0), which is not necessarily the airfoil’s 1/4 chord point.
Force calculation
The lift and moment coefficients CL, CM, are calculated by direct surface pressure integration:
/ _ / CL = L/q = | Cp dx CM = M/q = | -Cp [(x-xref) dx + (y-yref) dy]
/ /
_ where x = x cos(a) + y sin(a) ; a = angle of attack
_
y = y cos(a) - x sin(a)
The integrals performed in the counterclockwise direction around the airfoil contour. The pressure coefficient Cp is calculated using the Karman-Tsien compressibility correction.
The drag coefficient CD is obtained by applying the Squire-Young formula at the last point in the wake — NOT at the trailing edge.
(H+5)/2
CD = D/q = 2 Theta_i = 2 Theta (u/V)
| where Theta = momentum thickness | |
| u = edge velocity | at end of wake |
| H = shape parameter |
V = freestream velocity
Theta_i = momentum thickness at "downstream infinity"
The Squire-Young formula in effect extrapolates the momentum thickness to downstream infinity. It assumes that the wake behaves in a asymptotic manner downstream of the point of application.
This assumption is strongly violated in the near-wake behind an airfoil with trailing edge separation, but is always reasonable some distance behind the airfoil. Hence, the usual application of Squire-Young at the trailing edge is questionable with separation present, but its application at the last wake point (typically 1 chord downstream) is always reasonable. Also, application at the last wake point also results in the formula having a smaller effect in any case, since there u ~ V, and hence Theta_i ~ Theta.
In most 2-D airfoil experiments, drag is measured indirectly by measuring 2 Theta/c in the wake, often within one chord of the airfoil’s trailing edge. For consistency, this should be compared to the Theta value predicted by XFOIL at the same wake location, rather than the “true” Cd = 2 Theta_i/c value which is effectively at downstream infinity. In general, Theta_i will be smaller than Theta. In most airfoil drag measurement experiments, this difference may amount to the drag measurement being several percent too large, unless some correction is performed.
In addition to calculating the total viscous CD from the wake momentum thickness, XFOIL also determines the friction and pressure drag components CDf,CDp of this total CD. These are calculated by
/ _ CDf = | Cf dx CDp = CD - CDf
/
Here, Cf is the skin friction coefficient defined with the freestream dynamic pressure, not the BL edge dynamic pressure commonly used in BL theory. Note that CDp is deduced from CD and CDf instead of being calculated via surface pressure integration. This conventional definition
/ _ CDp = | Cp dy
/
is NOT used, since it is typically swamped by numerical noise.
Transition criterion
Transition in an XFOIL solution is triggered by one of two ways:
free transition: e^n criterion is met forced transition: a trip or the trailing edge is encountered
The e^n method is always active, and free transition can occur upstream of the trip. The e^n method has the user-specified parameter “Ncrit”, which is the log of the amplification factor of the most-amplified frequency which triggers transition. A suitable value of this parameter depends on the ambient disturbance level in which the airfoil operates, and mimics the effect of such disturbances on transition. Below are typical values of Ncrit for various situations.
situation Ncrit ----------------- ----- sailplane 12-14 motorglider 11-13 clean wind tunnel 10-12 average wind tunnel 9 <= standard "e^9 method" dirty wind tunnel 4-8
Note: The e^n method in XFOIL is actually the simplified envelope version, which is the same as the full e^n method only for flows with constant H(x). If H is not constant, the two methods differ somewhat, but this difference is typically within the uncertainty in choosing Ncrit.
The e^n method is only appropriate for predicting transition in situations where the growth of 2-D Tollmien-Schlichting waves via linear instability is the dominant transition-initiating mechanism.
Fortunately, this happens to be the case in a vast majority of airfoil applications. Other possible mechanisms are:
- Crossflow instabilities. These occur on swept wings with significant
favorable chordwise pressure gradients. - Attachment-line transition. This requires large sweep, large LE radius, and a large Reynolds number. Occurs primarily on big jets.
- Bypass transition. This occurs in cases with sufficient wall roughness and/or large freestream turbulence or vibration levels. The linear-instability phase predicted by the e^n method is “bypassed”, giving relatively early transition. Usually occurs in favorable pressure gradients, while the linear-instability mechanism usually dominates in adverse pressure gradients.
If any of these alternative transition mechanisms are present, the trips must be set to mimick their effect. The bypass transition mechanism can be mimicked to some extent by the e^n method by setting Ncrit to a small value — Ncrit=1 or less. This will cause transition just after linear instability begins. For very large freestream turbulence or roughness in favorable pressure gradients, bypass transition can occur before the linear instability threshold, and in this case trips will have to be set as well.