1 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 = 3106, 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.) Problem 2 on next 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 = 3106, 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. Problem 3 on next page → 5 Problem 3. For this question you will analyze the pressure coefficient, p. Again, consider the NACA 2412 from Problem 1. To save you time, I have used XFLR5 to produce a plot of the Cp distributions on the upper and lower sides of the airfoil, for both = –2 (red) and 5 (blue). You will use this plot below to answer the following question. Figure for Problem 3. vs. x/c for = –2° and 5 for an NACA 2412 airfoil. (Note: In aeronautical engineering, it is typical to reverse the p (or y) axis for the p plot, i.e. negative values are above and positive ones are below, so that when the airfoil is producing positive lift, it is more clear which pressure distribution corresponds to its upper surface, and which is for the bottom surface. Also, the top side of the airfoil is called the “suction side,” and the bottom is called the “pressure side.”) It is very important that you know that for = –2, ≈ 0. a) For the = 5 curves of p: are the upper- and lower-side p distributions consistent with what you would expect for an airfoil generating lift? (Here I do not tell you which of the blue curves is for the upper side and which is for the lower side, but you can reason it out from the physics.) b) For the = –2 curves of p: are the upper- and lower-side p distributions consistent with what you would expect for this cambered airfoil if it is producing nearly 0 lift? Please explain your answer, discussing what you would expect p curves to look like for 0 lift, and specifically how you would expect the two (upper and lower) curves to compare for this cambered airfoil. You will only receive full credit if you address all these points. Hints for part (b) on next page: 0 0.2 0.4 0.6 0.8 1 x/c -2 -1.5 -1 -0.5 0 0.5 1 C p = -2 o = 5 o Curve for upper airfoil side Curve for lower airfoil side Is this the curve for the upper or lower side? Is this the curve for the upper or lower side? 6 Hint 1: I’m not asking about the fine details of the shape of each pressure distribution, think more simply: namely, does it make sense that the distributions are different, and why? Hint 2: remember, this is a cambered airfoil (non-symmetric geometry)—please keep this in mind in your discussion of pressure distributions and how they produce the total lift force. Hint 3: there is nothing special or meaningful about the feature where the two curves cross over at x/c = 0.2. The curves are on different sides of the airfoil, this is not an important feature. (If you wanted to produce this plot yourself in the future, here is some helpful information. To export the p graph data, right-click on it, choose “Cp graph”, then “Export Graph” which will produce a .csv file. To get the data for only one , make sure that operating point for the desired is selected in the drop-down menu that is the 2nd to the right from the one specifying the airfoil. Then, if there are still multiple p curves shown, right-click on the p plot and choose “Show Current Op Only”—then do the export operation, and the .csv file will have the p data for only the you selected.)
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