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日期:2022-04-13 09:52

MAE 424: Aerodynamics, Spring 2022

Project #2: Due Fri 4/15/2022 at 11:59pm EDT via electronic submission


YOU MUST SUBMIT 1 PDF FILE OF YOUR SOLUTION; ANY OTHER SUBMISSION

TYPE OR SUBMISSION OF MULTIPLE FILES WILL RESULT IN A SCORE OF 0.


This project will give you a chance to explore airfoil concepts we covered (and will cover) in class

by using publicly-available software, XFLR5. It is based on MIT’s XFOIL program and is covered

in a separate tutorial (MAE424-Project-Tutorial.pdf) posted on UBLearns. This file will give you

an introduction to the software as well as links for obtaining it. NOTE: this tutorial is from

2014—although not much has changed in XFLR5, it is always possible that some minor

details are different. Only focus on the airfoil analysis portion of the tutorial, and on the

XFLR5 content and nothing else—and disregard the old due dates in the tutorial!


There is plenty of information online on XFLR5, please visit its main page which includes helpful

documentation (but the main tabs and video link don’t work…): http://www.xflr5.com/xflr5.htm

There’s a non-secure page (xflr5.tech); I’ve pulled the YouTube links below, no need to use it!!!

Download page is here: https://sourceforge.net/projects/xflr5/files/

YouTube links to video tutorials:

https://www.youtube.com/playlist?list=PLtl5ylS6jdP6uOxzSJKPnUsvMbkmalfKg

https://www.youtube.com/playlist?list=PLtl5ylS6jdP6_64SKRoOJUfuEooHRWNUO

The original XFOIL is still maintained here: https://web.mit.edu/drela/Public/web/xfoil/


FORMATTING:

You will submit 1 pdf file only (no other formats are accepted, multiple files will not be

accepted).

You must use a word-processing program—no handwritten solutions will be allowed.

Each figure (plot) must have a caption below it, clearly identifying the figure and its

contents (do not use figure “titles” above them—this is very uncommon).

Figures must have legends identifying what each plotted line or quantity is.

Figures must be numbered or identified as belonging to which part of which problem.

In your plots, you must use the specified line colors and line styles, otherwise the

reports will be impractical to grade.

Briefly answer the discussion questions—your answers should be no longer (and no

shorter) than they need to be.

You are NOT required to have a title page, introduction, or conclusions.

Please organize your document neatly and clearly; the reader should not have to “hunt

around” for the answers, or wonder which plot belongs to which part.

All engineering reports have such content and requirements; you show integrity and

professionalism by producing a document that your colleagues would find acceptable.


One thing about XFOIL and XFLR5: they incorporate viscous BL effects and can predict

BL transition (from laminar to turbulent), drag, flow separation, and stall. However, certain

parameters need to be adjusted in the program to do this well, and I just used the default

values—therefore you will see greater differences between the XFLR5 modeling predictions

vs. experiments when it comes to stall behavior. If I had spent more time adjusting these

parameters the performance would be improved, but it takes a lot of effort!

2

Exporting data: to produce the plots for this project and compare different curves (cases), you will

need to export the XFLR5 data to e.g. a text file that can be read by Excel or Matlab.


See the tutorial, but for the lift, drag, etc., polars, one way to do this is to click on “Polars” in the

top menu bar → “Current Polar” → “Export” and choose for example a .csv file. Also, you can

click on “Polars” in the top menu bar → “Export all” → “to text format” and you should also get a

.csv file. Additionally, you can right-click in the XFLR5 polar window to perform the export.


In the output file, you will see some “header” lines then columns of variables like , , and xcp,

and rows for each operating point, i.e. angle of attack, ?.


Last comment: if any of the input parameters you need for your analysis are not here in this

document, please use the default values you see in the supplied tutorial.



Problem 1. For this question you will make a detailed examination of the NACA 2412 airfoil,

comparing results from XFLR5, thin-airfoil theory, and experimental data.


a) Using XFLR5, compute the performance of this airfoil for M = 0.0, Re = 3?106, and NCrit =

9.0, for the angle of attack range ? = –10? to 20?, using the default 100 panels. Choose a 0.5?

increment in ? to get reasonable curves.


Hint: to test only one Re value, use “Analysis” → “Batch Analysis” → “Analysis Type 1,” put

in 3,000,000 for the Min Re, 3,000,000 for the Max Re, and some non-zero Re increment like

1,000—it will still calculate the airfoil results for only one Re.


Note: what is the purpose of the box “Store OpPoints”? It allows you to plot the p—but I do

not ask you to do that, I just provide you the p plot in Problem 3.


Part (a) here is just an analysis step, the required plot is given in part (b). Sometimes operating

points do not converge—first try to increase the number of iterations, perhaps to 500 or 1,000.

If this does not work, check the plots to see if the behavior is strange at that ?, if not, then do

not worry about it. If you want to delve further into this convergence issue, please see the

video tutorials accessible from the XFLR5 web page (link above).


b) As mentioned above, it is best to export the required XFLR5 data and plot it on your own, for

maximum flexibility. Plot the following quantities on the same figure (all quantities should be

produced by XFLR5 unless otherwise noted):

1) vs. ? (red solid line); plot ? in degrees, not radians.

2) The theoretical (inviscid) vs. ? curve from thin airfoil theory (red dashed line). For

a cambered thin airfoil, = 2?? + ,0, where ,0 is the lift coefficient at ? = 0?.

Instead of calculating ,0 (which we could with an equation for the camber line), we

will use the experimental value, which is ,0 ? 0.225 (see experimental data below).

3) vs. ? (solid green line).

3

4) m,c/4 vs. ? (solid blue line); in XFLR5, Cm is m,c/4.

5) xcp vs. ? (solid magenta).

6) The experimental vs. ? data (solid black line).


The experimental NACA 2412 data are below, in 2 rows (each ? has a corresponding

)?


?(?)? -4.2 -2.0 0.1 2.1 4.1 6.0 8.0 10.0 12.0 14.1 15.1 16.1 16.3 18.3

: -0.185 0.04 0.225 0.445 0.645 0.86 1.065 1.255 1.43 1.585 1.59 1.545 1.505 1.215


(These NACA 2412 experimental data are at Re = 3.1 million—close enough to our

Re—and are originally from Abbott, I. H. & Von Doenhoff, A. E., “Theory of Wing

Sections,” Dover, 1959. However, these experimental data are obtained more

accurately from NASA-CR-197497, which are the numbers I give here. In CR-197497,

the authors corrected the ? for infinite aspect ratio (AR); compare these results with the

right-hand NACA 2412 plot data from NACA TR 460 and see the methods section in

NACA TR 416.)


Next, please answer the following questions based on the part (b) plot:


c) How does the vs. ? curve from XFLR5 compare with the experimental NACA data?


d) How does the vs. ? curve from XFLR5 compare with thin airfoil theory (inviscid result)?

Over which ?-range are they different, and why do you think this difference occurs?


e) The m,c/4 (from XFLR5) is relatively constant vs. ? for low angles of attack—what does this

indicate about the quarter chord point (i.e. about x/c = 1/4)?


f) What causes the (from XFLR5) to increase substantially at high ?? (You may want to

zoom-in on the data yourself to get a closer look—but DO NOT make a second plot.)


g) The dimensionless xcp/c (from XFLR5) behaves strangely and “blows up” near a certain ? < 0

value. Why does this occur?


h) Away from this “blow-up” region (for ? > 0), does the xcp/c vary with changing ? or is it nearly

constant with changing ?? (Hint: look in the lecture notes to see what you would expect for a

cambered airfoil.)

page →

4

Problem 2. Here you will examine parametric trends in airfoil design. For all parts of the problem,

use XFLR5 and assume M = 0.0, Re = 3?106, and NCrit = 9.0 over a larger range of angles of

attack, ? = –10? to 25?.


a) Make a comparison of the NACA 2412, 2612, and 2812 airfoils by plotting the following (on

3 different plots): (1) vs. ?, (2) vs. ?, (3) ? vs. ?.


Use solid lines and red for NACA 2412, green for NACA 2612, and blue for NACA 2812.


1) Please make some brief comments on the effect of the maximum camber location on the

airfoil performance—be sure to comment on features you observe in each plot.


2) Real airfoils (and wings) have control surfaces that modify them. As the maximum camber

location increases, what configuration does this remind you of?



b) Make a comparison of the NACA 2412, 2408, and 2416 airfoils by plotting the following (on

3 different plots): (1) vs. ?, (2) vs. ?, (3) ? vs. ?.


Use solid lines and red for NACA 2412, green for NACA 2408, and blue for NACA 2416.


ALSO: on plot (1), include the theoretical inviscid thin-airfoil theory line from Problem 1(b):

= 2 + ,0 (with ,0 0.225 as before), using a dashed red line.


1) Please make some brief comments on the effect of thickness on the airfoil performance—

be sure to comment on features you observe in each plot.


2) Also, comment on how thickness affects the comparison with the thin-airfoil theory line.


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