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Post by Br. Marius on Feb 13, 2015 18:50:06 GMT
A hingeless rotor model of diameter 6 ft was tested in the Glenn L. Martin wind tunnel. The rotating flap frequency of the model was 1.1/rev, and the tip speed was 650 ft/sec. The tunnel speed is increased from 0 to 200 ft/sec, in steps of 25 ft/sec. The shaft angle is held fixed at +5 deg (forward). Calculate thrust and blade response (β0, β1c, and β1s), Assume Lock number of 5.0, lift-curve slope “a” of 5.7 and solidity ratio σ of .05.
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Post by Br. Marius on Feb 15, 2015 21:05:06 GMT
Is anyone else having an issue getting their solver to converge? I think that I've made all the necessary conversions between the HP and TPP, but I can't figure out what is messing up my code (I have only been messing with case A (question 1) figuring that I can apply the solution to 2 and 3 when I finish).
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Post by Deleted on Feb 16, 2015 20:48:08 GMT
Hmmmmm, I feel like it has something to do with the collective pitch. I think there's a mistake in the question and it should be given to us like in Example 1.2. I see that you initialized it as b1c, but I don't see where it's iteratively updated in Case A. Maybe that's it. Thing is, I'm not sure if collective is actually supposed to be iteratively solved or explicitly given to us.
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Post by Br. Marius on Feb 16, 2015 21:18:33 GMT
In reading the questions it seemed as though all control settings, including collective, should be left at zero. I say this because the flapping angles are supposed to be the results and, unless control settings are specified, it doesn't seem like you could get a specific flapping angle response. I think that ex 1.2 in the notes shows this too--the control settings have to be specified unless they are the "fallouts" and are determined by a specific flapping angle response.
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Post by Deleted on Feb 17, 2015 4:25:30 GMT
I will have to revisit this in the morning. My graphs are attached but I can not wrap my head around the negative thrust. It did converge
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Post by Deleted on Feb 17, 2015 16:30:54 GMT
This is my code. I dressed it up this morning so it can be easily followed. Attachments:ENAE633HW3Code.pdf (13.12 KB)
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Post by Deleted on Feb 17, 2015 17:21:02 GMT
My legends on the graphs are not correct. I corrected them you can see what I plotted did not correspond to the legend.
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Post by Deleted on Feb 17, 2015 19:15:01 GMT
Hm, something seems off in your hover solution for the flap response, Mario. Otherwise, our plots are the same. My thrust is also negative, but not quite as negative as yours. Maybe it makes sense because there's no collective pitch to produce thrust, so the incoming freestream flow is like a negative thrust?
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Post by Br. Marius on Feb 17, 2015 19:29:23 GMT
I think that makes sense, Justin--relative to the oncoming flow, the blades would have a negative AOA, generating thrust in the negative direction.
In other news...still working through code. Cleaned it up a little and implemented a few changes (thanks for posting, Mario), but still nothing. I just noticed that my flapping equations are much different than yours, though, Mario. Where did you get your expressions from?
% Wind Tunnel Rotor Control Response Solver % This solver can be utilized in the following modes: % --A-- Find flapping angles (given control deflections and geometry) % --B-- Find control angles (given flapping angles and geometry) % This solver implements BEMT
% Assumes a rotor with rectangular and untwisted blades; no precone angle
% Br. Marius Strom, TOR % ENAE633: Helicopter Dynamics
% Clean it up clear all close all commandwindow
%% Definitions and initialization
% Initialize geometry and aerodynamic variables with given information rho = 0.0023772;% Air density (slug/ft^3) Rmr = 3; % MR radius (ft) Amr = pi*Rmr^2; % MR area (ft^2) nub = 1.1; % Flapping frequency (/rev) lockno = 5; % Lock number cla = 5.7; % Lift curve slope (/rad) sigma = 0.05; % MR solidity vtipmr = 650; % MR tip speed (ft/s) alphas = -5:5:5;% Shaft angle (deg) alphas = alphas*2*pi/360; % Shaft angle converted to (rad) vtestmax = 200; % Maximum WT test speed (ft/s) kf = 1.15; % Fwd flight induced velocity correction factor kh = 1; % Hover induced velocity correction factor
% Define covergence tolerance and test variable for iterative solver tol = 10^-7; delta = 1;
% Define advance ratio range to test vtest = 0:25:vtestmax; mu = vtest / vtipmr; maxnum = size(mu,2);
% All cntl/flap resp. init. at 0 deg b1c = zeros(1,maxnum); b1s = b1c; b0 = b1c; t1c = b1c; t1s = b1c; t0 = b1c;
%% CASE A % Assume all control angles to be zero for(i=1:size(alphas,2)) li = mu.*tan(alphas(i)); % Initial value of inflow ratio while(delta>tol) % Each iteration updates inflow as loop variable % Cyclic flapping angles and shaft angles
% Eq. 1.27 in notes b0 = lockno*(0.125.*t0.*(1+mu.^2)+mu.*t1s/6-li/6)/(nub^2); b1c = lockno/(nub^2-1)*(0.125*(t1c-b1s).*(1+0.5*mu.^2)-mu.*b0/6); b1s = lockno/(nub^2-1)*(0.125*(t1s+b1c).*(1-0.5*mu.^2)+mu.*t0/3-... 0.25*mu.*li+0.25*t1s.*mu.^2);
% Update CT CT = 0.5*sigma*cla*(t0/3.*(1+1.5*mu.^2)+mu.*t1s*0.5-0.5*li); % Inflow update li = li+mu.*b1c; % Convert HP inflow to TPP for Eq. 1.47 mutpp = vtest.*cos(alphas(i)+b1c)/vtipmr; % Update TPP advance ratio % Eq. 1.47 implemented via a Newton-Rhapson solver for inflow % Define first derivative of the equation of interest for use in the % solver (i.e., 0 = d(ueq)/d(li)) mutpp(1)=mutpp(2); % To avoid errors during iteration ueqn = @(li) (li-(mutpp.*tan(alphas(i)+b1c)+kf*CT*0.5./sqrt(mutpp.^2+li.^2))); dueqn = @(li) (1+0.5*kf*CT.*li.*(mutpp.^2 + li.^2).^-1.5); test = newton(ueqn,dueqn,li,tol);
% Hover case (induced inflow correction factor varies from fwd flight) mutpp(1) = 0; test(1) = kh*sqrt(0.5*CT(1)); test = test-mutpp.*b1c; % Convert all to hub plane inflow
% Check for convergence delta = max(abs(test-li)); li = test; % Update loop variable end % Plot flapping angles figure(i) plot(vtest,b0*360/(2*pi),vtest,b1c*360/(2*pi),vtest,b1s*360/(2*pi),'LineWidth',2) ttext{i} = sprintf('WT Flapping Angles: \\alpha_s = %0.0f deg',alphas(i)*360/(2*pi)); end
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Post by Deleted on Feb 17, 2015 22:06:19 GMT
I first used eq 1.27 from his notes and then I used eq 1.56 which are derived from 1.27. all from his notes
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Post by Deleted on Feb 17, 2015 22:07:16 GMT
1.27 equations were abandoned in my code for 1.56 ones
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Post by Deleted on Feb 17, 2015 22:29:26 GMT
if you have a chance can you post your hover solution so I can see the difference. I am sort of lost on what to look for. Thanks
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Post by Deleted on Feb 17, 2015 22:35:11 GMT
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Post by Deleted on Feb 17, 2015 23:04:24 GMT
Here are my results and work. I checked it with a previous year's solutions, so this should be correct:
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Post by Deleted on Feb 18, 2015 0:53:44 GMT
Thanks Justin, Thrust was off because my radius was twice as big, he actually said diameter 6 ft out of habit I read radius. Also that "hover" noise was because I used 1 ft/sec steps but if I use 25 ft/sec then it goes away.
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