ME 5301 Term Project Aravind Baskar 03-04-2016 A0136344 1 | Page FLOW SYSTEM ANALYSIS Part – 1: Unsteady Kernel function for 3D incompressible potential flow Starting with the definition of acceleration potential, the equation for kernel function is derived and the steps are detailed as below:
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ME 5301 Term Project Aravind Baskar
03-04-2016 A0136344
1 | P a g e
FLOW SYSTEM ANALYSIS
Part – 1: Unsteady Kernel function for 3D incompressible potential flow
Starting with the definition of acceleration potential, the equation for kernel
function is derived and the steps are detailed as below:
ME 5301 Term Project Aravind Baskar
03-04-2016 A0136344
2 | P a g e
ME 5301 Term Project Aravind Baskar
03-04-2016 A0136344
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ME 5301 Term Project Aravind Baskar
03-04-2016 A0136344
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ME 5301 Term Project Aravind Baskar
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ME 5301 Term Project Aravind Baskar
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Part – 2: Tapered Wing – Analysis
The algorithm of the program sequence is briefly explained above. The grid
points are generated based on the slope of the lines and similarity principle. The
process to determine AIC involve the processes detailed in the referenced paper.
All relevant sub-routines are given by different files to aid debugging process. The
list of files used in the program is as follows:
Project_Final. m – Main File
getKappa.m, get I1.m, getI2.m, getI1pos.m, getI2pos.m – Subroutines
For various cases of reduced frequencies, the lift, moment and coefficients are
D:\National University Of Singapore...\PROJECT_FINAL.m Page 58 April, 2016 12:09:28 PM
(57,2))); % Avg. Chord Length %CL = Lift/(beta*S); % Non dimensional Coefficent of Lift %CM = MO/(beta*S*cavg); % Non dimensional Coefficient of Moment %disp(M);disp(k);display(num);display(Lift);display(MO);display(CL);display(CM);end
8/4/16 12:05 PM MATLAB Command Window 1 of 3
>> PROJECT_FINAL 0.5000 0.0860 num = 1 Lift = -38.2409 + 6.3813i MO = -7.8320e+02 + 4.5654e+02i CL = -0.0736 + 0.0123i CM = -0.1005 + 0.0586i 214 end 0.5000 0.1000 num = 2 Lift = -41.4994 +15.5025i MO = -8.1313e+02 + 7.0952e+02i CL = -0.0799 + 0.0298i
8/4/16 12:05 PM MATLAB Command Window 2 of 3
CM = -0.1043 + 0.0910i 0.5000 0.1140 num = 3 Lift = -42.7592 +25.3623i MO = -7.8959e+02 + 9.7169e+02i CL = -0.0823 + 0.0488i CM = -0.1013 + 0.1247i 0.5000 0.1280 num = 4 Lift = -42.0073 +35.4362i MO = -7.1395e+02 + 1.2293e+03i CL =
8/4/16 12:05 PM MATLAB Command Window 3 of 3
-0.0808 + 0.0682i CM = -0.0916 + 0.1577i >>
8/4/16 12:04 PM MATLAB Command Window 1 of 5
>> PROJECT_FINAL 0 0.0860 num = 1 Lift = -32.7946 +22.5023i MO = -6.4807e+02 + 8.5323e+02i CL = -0.0547 + 0.0375i CM = -0.0720 + 0.0948i 0 0.1000 num = 2 Lift = -34.3305 +33.6495i MO = -6.3530e+02 + 1.1559e+03i CL = -0.0572 + 0.0561i
8/4/16 12:04 PM MATLAB Command Window 2 of 5
CM = -0.0706 + 0.1284i 0 0.1140 num = 3 Lift = -33.7213 +45.3042i MO = -5.6543e+02 + 1.4620e+03i CL = -0.0562 + 0.0755i CM = -0.0628 + 0.1624i 0 0.1280 num = 4 Lift = -30.9916 +56.9340i MO = -4.4079e+02 + 1.7575e+03i CL =
8/4/16 12:04 PM MATLAB Command Window 3 of 5
-0.0517 + 0.0949i CM = -0.0490 + 0.1953i >> PROJECT_FINAL 0 0.0860 num = 1 Lift = -32.7946 +22.5023i MO = -6.4807e+02 + 8.5323e+02i CL = -0.0547 + 0.0375i CM = -0.0720 + 0.0948i 0 0.1000 num = 2 Lift = -34.3305 +33.6495i MO = -6.3530e+02 + 1.1559e+03i
8/4/16 12:04 PM MATLAB Command Window 4 of 5
CL = -0.0572 + 0.0561i CM = -0.0706 + 0.1284i 0 0.1140 num = 3 Lift = -33.7213 +45.3042i MO = -5.6543e+02 + 1.4620e+03i CL = -0.0562 + 0.0755i CM = -0.0628 + 0.1624i 0 0.1280 num = 4 Lift = -30.9916 +56.9340i
8/4/16 12:04 PM MATLAB Command Window 5 of 5
MO = -4.4079e+02 + 1.7575e+03i CL = -0.0517 + 0.0949i CM = -0.0490 + 0.1953i >>
D:\National University Of Singapore...\PROJECT_FINAL.m Page 18 April, 2016 12:09:28 PM
%% Flutter Analysis for Tapered Wing Geometry %%%% References : DLM Tools from University of Minnesota - http://gitpaaw.umnaem.webfactional.com/tools.git %%%% INITIALIZATIONrf = 0.086:0.014:0.128; % Reduced Frequencies for all cases %for num = 1:4 % Loop for Various Reduced Frequencies % rho = 2.38e-3; % Density of Air % M = 0.5; % Mach Number % k = rf(num); % For individual cases % sw = 40; % Span Length % ds = sw/8; % Increment Spanwise % slope_u = 0.1; % Slope dy/dx = 4/40 using median principle % slope_l = - slope_u; % Slope of symmetric opp. line%% GRID COORDINATESi = 0;j = 0;coordinate = zeros(63,4);panel = zeros(48,5); for t = 0:ds:sw; i = i+1; xl(i,:) = slope_u*t; % Lower Boundary % xu(i,:) = slope_l*t + 19; %#ok<*SAGROW> % Upper Boundary % dx(i,:) = (xu(i,1) - xl(i,1))/6; % Increment % xl_1(i,:) = xl(i,1) - dx(i,1); xu_1(i,:) = xu(i,1) - dx(i,1); for q = xl_1(i,1):dx(i,1):xu_1(i,1); j = j+1; n(j,:) = j; y(j,:) = t; x_1(j,:) = q + dx(i,1); coordinate(j,1) = n(j,1); % Node Number % coordinate(j,2) = x_1(j,1); % Chordwise Coordinate % coordinate(j,3) = y(j,1); % Spanwise Coordinate % end endh = 0;%% PANELS for PB = 1:1:48; if(PB==7) h = 7; end if (PB==13) h = 14; end if(PB==19) h = 21; end if(PB==25) h = 28; end if(PB==31) h = 35;
D:\National University Of Singapore...\PROJECT_FINAL.m Page 28 April, 2016 12:09:28 PM
D:\National University Of Singapore...\PROJECT_FINAL.m Page 58 April, 2016 12:09:28 PM
(57,2))); % Avg. Chord Length %CL = Lift/(beta*S); % Non dimensional Coefficent of Lift %CM = MO/(beta*S*cavg); % Non dimensional Coefficient of Moment %disp(M);disp(k);display(num);display(Lift);display(MO);display(CL);display(CM);end