quasi mat lab

7/24/2019 Quasi Mat Lab

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%Generalized Quasi-One-Dimensional (QOD) Flow Analyzer%by Adam J. Resler

%This program designed for subsonic flow only (0 < M < 1).

%Clear variables and screen for clean run of programclcclear

%Fluid informationga = 1.4; %input(' Input heat capacity ratio, gamma: ');gm = 0.5 * (ga - 1);gi = ga / (ga - 1);

%Gather initial information

%Data from test cases%case1%case2%case3

%case4

%Data from project caseme560p1case

%Set tolerance for convergenceelim = 0.005; %input('Tolerance, eps_lim: ');

%Perform initial calculationsto1 = t1 * (1 + gm * m1^2);po1 = p1 * ((1 + gm * m1^2)^gi);a1 = 3.1415926535897932 * (d1^2) / 4;dx = l / (n - 1);

%Initialize variablesx(1) = 0;m(1) = m1;mtest(1) = m1;p(1) = p1;po(1) = po1;t(1) = t1;to(1) = to1;a(1) = a1;d(1) = d1;i = 1;j = 1;eps = 1;

sonic = 0;stag = 0;slow = 0;dad = -0.0000084667;dexit = d1 + ad * l;

%Begin looptic

% Optional exit diameter loop for choked conditions


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% To disable diameter finding loop, place a '%' figure in front of lines% 71, 73, 161, 162, and 164 in this code.%while sonic == 0

%eps = 1;

while eps >= elim

i = 1;

while i < n;% Solve for lagging variablesdadx(i) = 1.5707963267948966 * d(i) * (ad + 2 * bd * x(i));dtdx(i) = ae + 2 * be * x(i);g(i) = (-2 * dadx(i) / a(i)) + ((ga * (m(i)^2) + 1) * dtdx(i) /

to(i)) + (ga * (m(i)^2) * f * 4 / d(i));dmdx(i) = (m(i)^2) * (((1 + gm * (m(i)^2)) * g(i)) / (1 -

(m(i)^2)));

% Solve for new variables

m(i+1) = ((m(i)^2) + dmdx(i) * dx)^0.5;

% Test for sonic conditions from subsonicif m1 < 1 && m(i+1) >= 0.9999

m(i+1) = 0.9999;

if sonic == 0xson = x(i-1);dson = d(i-1);

end

sonic = 1;

end

%Test for sonic conditions from supersonicif m1 > 1 && m(i+1)


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stag = 1;

end

x(i+1) = x(i) + dx;to(i+1) = to(1) + ae * x(i+1) + be * (x(i+1)^2);d(i+1) = d(1) + ad * x(i+1) + bd * (x(i+1)^2);a(i+1) = 3.1415926535897932 * (d(i+1)^2) / 4;t(i+1) = t(i) * (((1 + gm * (m(i)^2)) * (to(i+1))) / ((1 + gm *

(m(i+1)^2)) * to(i)));p(i+1) = (p(i) * m(i) * a(i) / (m(i+1) * a(i+1))) *

((t(i+1)/t(i))^0.5);i = i + 1;

end

mtest(j) = m(i);dmdxt(j) = dmdx(i-1);ttest(j) = t(i);

ptest(j) = p(i);

% Test convergence of Mach numberif j > 1

eps = abs((mtest(j) - mtest(j-1))/mtest(j));e(j) = eps;

if eps > elimdx = l / (n - 1);

end

end

j = j + 1;n = n + 1;

end

%ad = ad + dad;%dexit = d1 + (ad * l);

%end

% Negate fencepost problemj = j - 1;n = n - 1;

% Analysis and screen printue = m(n-1) * sqrt(ga * 287 * t(n-1));

% Plotting resultssubplot(3,1,1); plot(x,m,'LineWidth',1.5),xlabel('Duct Position(m)'),ylabel('Mach Number'),grid on,xlim([0 l]);set(gca,'xtick',[0:l/20:l]);subplot(3,1,2); plot(x,t,'LineWidth',1.5),xlabel('Duct Position(m)'),ylabel('Static Temperature (K)'),grid on,xlim([0 l]);


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hold onplot(x,to,'r--','LineWidth',2.25),legend('Static Temperature','StagnationTemperature','Location',[0.132833333333323 0.539854166666662 0.240.0729694444444444]);hold offset(gca,'xtick',[0:l/20:l]);subplot(3,1,3); plot(x,p,'LineWidth',1.5),xlabel('Duct Position(m)'),ylabel('Static Pressure (Pa)'),grid on,xlim([0 l]);set(gca,'xtick',[0:l/20:l]);

% Print results

% Transition test resultsif sonic > 0

fprintf('Flow became CHOKED at approximately% 4.4f m in theduct.\n\n',xson);end

if slow > 0fprintf('Flow SLOWED TO SONIC at approximately% 4.4f m in the

duct.\n\n',xslo);end

if stag > 0fprintf('Flow became STAGNANT at approximately% 4.4f m in the

duct.\n\n',xstag);end

% Program resultsfprintf(' Exit Mach number: % 12.4f\n',m(n));fprintf(' Exit velocity: % 12.4f m/s \t or % 12.4f mph\n',ue,ue *2.23693629);fprintf(' Exit temperature: % 12.4f K \t\t or % 12.4f degF\n',t(n),(t(n)+273)*1.8 + 32);

% Pressure results and unit check (Pa, kPa, MPa); P > 0if p(n) >= 0 && p(n) < 1000

fprintf(' Exit pressure: % 12.4f Pa \t or % 12.4fpsi\n\n',p(n),p(n)*0.0001450377380072);elseif p(n) >= 1000 && p(n) < 1000000

p(n) = p(n)/1000;fprintf(' Exit pressure: % 12.4f kPa \t or % 12.4f

psi\n\n',p(n),p(n)*0.0001450377380072*1000);else

p(n) = p(n)/1000000;fprintf(' Exit pressure: % 12.4f MPa \t or % 12.4f

psi\n\n',p(n),p(n)*0.0001450377380072*1000000);

end

% Print inlet/exhaust diametersfprintf(' Inlet Diameter: % 12.2f mm \t or % 12.4f in.\n',d1 *1000,(d1*1000)*0.03937007874);fprintf(' Exhaust Diameter: % 12.2f mm \t or % 12.4f in.\n',dexit *1000,(dexit*1000)*0.03937007874);fprintf('\n');

% Program Analysis Time and Data


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fprintf('------------------------------------------------------------------\n');fprintf(' ********** PROGRAM ANALYSIS DATA **********\n');fprintf('\n');fprintf(' CPU Analysis Time: \t % 12.4f seconds\n',toc);fprintf(' Initial No. Iterations: \t % 12i\n',n1);fprintf(' Final No. Iterations: \t % 12i\n',n);fprintf(' Final tolerance: \t % 12.4E {limit % 12.4E}\n',eps,elim);fprintf('------------------------------------------------------------------\n');

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