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Turbine_Proj_V2.m
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%% AME 415 Turbine Sizing Code
% by Loren and Kaylyn
%% Cleaning
clear; clc;
%% Constants
g0 = 9.807; % [m/s^2]
m2ft = 3.2801;
hp2w = 745.699872;
%% Inputs
T01 = 500; % [K]
P01 = 13842074; % [Pa]
P3 = 11011992; % [Pa]
mdot = 13.61; % [kg/s]
M1 = 0.05;
c_p = 15636.11; % [J/kg/K]
gam = 1.3994;
R = 4123.311;
z = 1;
Zwiff = 0.8;
power = 6215; % [HP]
N = 50000; % [RPM]
%% Inputs for Loop 1
eta_TT = 0.90;
Nb_stator = 90; Nb_rotor = 100;
BL = 0.9;
phi = 0.4; psi = 1.6;
Rc = 0.4;
KlossN = 0.98; KlossR = 0.98;
%% Calculations
eta_TT_old = 0;
i=0;
ii=0;
while (abs(eta_TT_old-eta_TT)>0.001)
i=i+1;
UoverC0 = sqrt(1 / (phi^2 - 4*(Rc - 1)/eta_TT));
T3is = T01*(P3/P01)^((gam-1)/gam);
C0 = sqrt(2*c_p*(T01 - T3is));
U = C0*UoverC0;
Ca = U*phi;
dh0is = (C0^2 - Ca^2)/2;
W = eta_TT*dh0is;
power_est = mdot*W/hp2w;
alpha1 = 90;
alpha2 = atand(U*Ca/W);
C2 = Ca/sind(alpha2);
C2u = Ca/tand(alpha2);
C2a = Ca;
W2u = C2u - U;
W2a = Ca;
W2 = sqrt(W2u^2 + W2a^2);
alpha2p = atand(W2a/W2u);
W3a = Ca;
W3u = -U;
W3 = sqrt(W3a^2 + W3u^2);
C3a = Ca;
C3u = 0;
C3 = Ca;
alpha3 = 90;
alpha3p = atand(W3a/W3u);
T2 = T01 - (C2^2 / 2 / c_p);
a2 = sqrt(gam*R*T2);
M2 = C2/a2;
Mw2 = W2/a2;
Tw2 = T2*(1 + 0.5*(gam-1)*Mw2^2);
T3 = Tw2 - (W3^2 / 2 / c_p);
a3 = sqrt(gam*R*T3);
Mw3 = W3/a3;
M3 = C3/a3;
P02 = P01*KlossN;
P2 = P02/(1 + 0.5*(gam-1)*M2^2)^(gam/(gam-1));
Pw2 = P2*(1 + 0.5*(gam-1)*Mw2^2)^(gam/(gam-1));
Pw3 = Pw2*KlossR;
P3veri = Pw3/(1+ 0.5*(gam-1)*Mw3^2)^(gam/(gam-1));
rho2 = P2/z/R/T2;
rho3 = P3/z/R/T3;
rhor = (rho2+rho3)/2;
A2 = mdot/rho2/C2a;
A3 = mdot/rho3/C3a;
rmean = 30*U/pi/N;
L2 = A2/2/pi/rmean/BL;
L3 = A3/2/pi/rmean/BL;
%% Stator
sc0_stator = 0.427 + alpha2/58 - (alpha2/93)^2;
sBz_stator = Zwiff/(2*(sind(alpha2)^2)*(cotd(alpha2) - cotd(alpha1)));
s_stator = 2*pi*rmean/Nb_stator;
Bz_stator = s_stator/sBz_stator; c_stator = s_stator/sc0_stator;
betaS_stator = asind(Bz_stator/c_stator);
%% Rotor
sc0_rotor = 0.427 + abs(alpha3p)/58 - (alpha3p/93)^2;
sc1_rotor = 0.224 + (1.575 - abs(alpha3p)/90)*(abs(alpha3p)/90);
zeta = (90 - abs(alpha2p))/(90 - abs((alpha3p)));
sc_opt = sc0_rotor + (sc1_rotor - sc0_rotor)*abs(zeta)*zeta;
sBz_rotor = Zwiff/(2*(sind(alpha3p)^2)*(cotd(alpha2p) - cotd(alpha3p)));
s_rotor = 2*pi*rmean/Nb_rotor;
Bz_rotor = s_rotor/sBz_rotor; c_rotor = s_rotor/sc_opt;
betaS_rotor = asind(Bz_rotor/c_rotor);
eta_TT_old = eta_TT;
%% 3D Design
r_tip_stator = rmean + 0.5*L2; r_tip_rotor = rmean + 0.5*L3;
r_hub_stator = rmean - 0.5*L2; r_hub_rotor = rmean - 0.5*L3;
U_tip = r_tip_stator*pi*N/30;
U_hub = r_hub_stator*pi*N/30;
C2u_tip = rmean*C2u/r_tip_stator; C2a_tip = Ca;
C2u_hub = rmean*C2u/r_hub_stator; C2a_hub = Ca;
C2_tip = sqrt(C2u_tip^2 + C2a_tip^2);
C2_hub = sqrt(C2u_hub^2 + C2a_hub^2);
W2u_tip = C2u_tip - U_tip; W2a_tip = C2a_tip;
W2_tip = sqrt(W2u_tip^2 + W2a_tip^2);
W2u_hub = C2u_hub - U_hub; W2a_hub = C2a_hub;
W2_hub = sqrt(W2u_hub^2 + W2a_hub^2);
alpha2_tip = asind(C2a_tip/C2_tip); alpha2p_tip = atand(W2a_tip/W2u_tip);
alpha2_hub = asind(C2a_hub/C2_hub); alpha2p_hub = atand(W2a_hub/W2u_hub);
C3u_tip = 0; C3a_tip = Ca;
C3u_hub = 0; C3a_hub = Ca;
C3_tip = sqrt(C3u_tip^2 + C3a_tip^2);
C3_hub = sqrt(C3u_hub^2 + C3a_hub^2);
W3u_tip = C3u_tip - U_tip; W3a_tip = C3a_tip;
W3_tip = sqrt(W3u_tip^2 + W3a_tip^2);
W3u_hub = C3u_hub - U_hub; W3a_hub = C3a_hub;
W3_hub = sqrt(W3u_hub^2 + W3a_hub^2);
alpha3_tip = asind(C3a_tip/C3_tip); alpha3p_tip = atand(W3a_tip/W3u_tip);
alpha3_hub = asind(C3a_hub/C3_hub); alpha3p_hub = atand(W3a_hub/W3u_hub);
tipVals = [C2a_tip, C2u_tip, C2_tip, W2a_tip, W2u_tip, W2_tip, ...
alpha2_tip, alpha2p_tip, C3a_tip, C3u_tip, C3_tip, ...
W3a_tip, W3u_tip, W3_tip, alpha3_tip, alpha3p_tip];
hubVals = [C2a_hub, C2u_hub, C2_hub, W2a_hub, W2u_hub, W2_hub, ...
alpha2_hub, alpha2p_hub, C3a_hub, C3u_hub, C3_hub, ...
W3a_hub, W3u_hub, W3_hub, alpha3_hub, alpha3p_hub];
meanVals = [C2a, C2u, C2, W2a, W2u, W2, alpha2, alpha2p, ...
C3a, C3u, C3, W3a, W3u, W3, alpha3, alpha3p];
%% Y Loss Stator
%Yp1
Yp1_stator = Y_p1calc(sc0_stator,alpha2);
%Yp2
Yp2_stator = Y_p2calc(sc0_stator,alpha2);
%Yp
mu_stator = 8.756E-6*((293.85+72)/(T2+72))*(T2/293.85)^(3/2);
nu_stator = mu_stator/rho2;
Yp_stator = Ypcalc(alpha1,alpha2,M1,M2,C2,c_stator,nu_stator,Yp1_stator,Yp2_stator);
%Ys Stator
Lc_stator = L2/c_stator;
Ys_stator = Y_Scalc(alpha1,alpha2,alpha1,Lc_stator,sc0_stator);
% Ycl Stator
Ycl_stator = 0;
% Yex Stator
Yex_stator = 0;
%Y Total
Y_N = Yp_stator + Ys_stator + Ycl_stator + Yex_stator;
%% Y Loss Rotor
%Yp1
Yp1_rotor = Y_p1calc(sc_opt,alpha3p);
%Yp2
Yp2_rotor = Y_p2calc(sc_opt,alpha3p);
%Yp
mu_rotor = 8.756E-6*((293.85+72)/(T3+72))*(T3/293.85)^(3/2);
nu_rotor = mu_rotor/rhor;
Yp_rotor = Ypcalc(alpha2p,alpha3p,Mw2,Mw3,W3,c_rotor,nu_rotor,Yp1_rotor,Yp2_rotor);
% Ys Rotor
Lc_rotor = L3/c_rotor;
Ys_rotor = Y_Scalc(alpha2p,alpha3p,alpha2p,Lc_rotor,sc_opt);
% Ycl Rotor
dL_rotor = 0.00025 / L3;
Ycl_rotor = Y_CLcalc(alpha2p,alpha3p,Lc_rotor,sc_opt,dL_rotor,1);
% Yex Rotor
Yex_rotor = 0;
% Y Total
Y_R = Yp_rotor + Ys_rotor + Ycl_rotor + Yex_rotor;
%% First Pass
M2_func = Mach2_calc(gam,M2);
P2_it = P01/((M2_func*(Y_N+1))-Y_N);
P02_it = P2_it * M2_func;
Mw3_func = Machw3_calc (gam,Mw3);
M3_func = Mach3_calc (gam,M3);
P3_it = Pw2/((Mw3_func*(Y_R+1))-Y_R);
Pw3_it = P3_it * Mw3_func;
P03_it = P3_it * M3_func;
Kloss_stator = P02_it/P01;
Kloss_rotor = Pw3_it/Pw2;
KlossN = Kloss_stator;
KlossR = Kloss_rotor;
while (abs (P3veri - P3) >100)
ii=ii+1;
C2_it = C2*(P3_it/P3);
Ca_it = C2_it*sind(alpha2);
C2 = C2_it;
Ca = Ca_it;
C2u = Ca/tand(alpha2);
C2a = Ca;
W2u = C2u - U;
W2a = Ca;
W2 = sqrt(W2u^2 + W2a^2);
alpha2p = atand(W2a/W2u);
W3a = Ca;
W3u = -U;
W3 = sqrt(W3a^2 + W3u^2);
C3a = Ca;
C3u = 0;
C3 = Ca;
alpha3 = 90;
alpha3p = atand(W3a/W3u);
T2 = T01 - (C2^2 / 2 / c_p);
a2 = sqrt(gam*R*T2);
M2 = C2/a2;
Mw2 = W2/a2;
Tw2 = T2*(1 + 0.5*(gam-1)*Mw2^2);
T3 = Tw2 - (W3^2 / 2 / c_p);
a3 = sqrt(gam*R*T3);
Mw3 = W3/a3;
M3 = C3/a3;
P02 = P01*Kloss_stator;
P2 = P02/(1 + 0.5*(gam-1)*M2^2)^(gam/(gam-1));
Pw2 = P2*(1 + 0.5*(gam-1)*Mw2^2)^(gam/(gam-1));
Pw3 = Pw2*Kloss_rotor;
P3veri = Pw3/(1+ 0.5*(gam-1)*Mw3^2)^(gam/(gam-1));
rho2 = P2/z/R/T2;
rho3 = P3/z/R/T3;
rhor = (rho2+rho3)/2;
A2 = mdot/rho2/C2a;
A3 = mdot/rho3/C3a;
rmean = 30*U/pi/N;
L2 = A2/2/pi/rmean/BL;
L3 = A3/2/pi/rmean/BL;
%% Stator
sc0_stator = 0.427 + alpha2/58 - (alpha2/93)^2;
sBz_stator = Zwiff/(2*(sind(alpha2)^2)*(cotd(alpha2) - cotd(alpha1)));
s_stator = 2*pi*rmean/Nb_stator;
Bz_stator = s_stator/sBz_stator; c_stator = s_stator/sc0_stator;
betaS_stator = asind(Bz_stator/c_stator);
%% Rotor
sc0_rotor = 0.427 + abs(alpha3p)/58 - (alpha3p/93)^2;
sc1_rotor = 0.224 + (1.575 - abs(alpha3p)/90)*(abs(alpha3p)/90);
zeta = (90 - abs(alpha2p))/(90 - abs((alpha3p)));
sc_opt = sc0_rotor + (sc1_rotor - sc0_rotor)*abs(zeta)*zeta;
sBz_rotor = Zwiff/(2*(sind(alpha3p)^2)*(cotd(alpha2p) - cotd(alpha3p)));
s_rotor = 2*pi*rmean/Nb_rotor;
Bz_rotor = s_rotor/sBz_rotor; c_rotor = s_rotor/sc_opt;
betaS_rotor = asind(Bz_rotor/c_rotor);
%% 3D Design
r_tip_stator = rmean + 0.5*L2; r_tip_rotor = rmean + 0.5*L3;
r_hub_stator = rmean - 0.5*L2; r_hub_rotor = rmean - 0.5*L3;
U_tip = r_tip_stator*pi*N/30;
U_hub = r_hub_stator*pi*N/30;
C2u_tip = rmean*C2u/r_tip_stator; C2a_tip = Ca;
C2u_hub = rmean*C2u/r_hub_stator; C2a_hub = Ca;
C2_tip = sqrt(C2u_tip^2 + C2a_tip^2);
C2_hub = sqrt(C2u_hub^2 + C2a_hub^2);
W2u_tip = C2u_tip - U_tip; W2a_tip = C2a_tip;
W2_tip = sqrt(W2u_tip^2 + W2a_tip^2);
W2u_hub = C2u_hub - U_hub; W2a_hub = C2a_hub;
W2_hub = sqrt(W2u_hub^2 + W2a_hub^2);
alpha2_tip = asind(C2a_tip/C2_tip); alpha2p_tip = atand(W2a_tip/W2u_tip);
alpha2_hub = asind(C2a_hub/C2_hub); alpha2p_hub = atand(W2a_hub/W2u_hub);
C3u_tip = 0; C3a_tip = Ca;
C3u_hub = 0; C3a_hub = Ca;
C3_tip = sqrt(C3u_tip^2 + C3a_tip^2);
C3_hub = sqrt(C3u_hub^2 + C3a_hub^2);
W3u_tip = C3u_tip - U_tip; W3a_tip = C3a_tip;
W3_tip = sqrt(W3u_tip^2 + W3a_tip^2);
W3u_hub = C3u_hub - U_hub; W3a_hub = C3a_hub;
W3_hub = sqrt(W3u_hub^2 + W3a_hub^2);
alpha3_tip = asind(C3a_tip/C3_tip); alpha3p_tip = atand(W3a_tip/W3u_tip);
alpha3_hub = asind(C3a_hub/C3_hub); alpha3p_hub = atand(W3a_hub/W3u_hub);
tipVals = [C2a_tip, C2u_tip, C2_tip, W2a_tip, W2u_tip, W2_tip, ...
alpha2_tip, alpha2p_tip, C3a_tip, C3u_tip, C3_tip, ...
W3a_tip, W3u_tip, W3_tip, alpha3_tip, alpha3p_tip];
hubVals = [C2a_hub, C2u_hub, C2_hub, W2a_hub, W2u_hub, W2_hub, ...
alpha2_hub, alpha2p_hub, C3a_hub, C3u_hub, C3_hub, ...
W3a_hub, W3u_hub, W3_hub, alpha3_hub, alpha3p_hub];
meanVals = [C2a, C2u, C2, W2a, W2u, W2, alpha2, alpha2p, ...
C3a, C3u, C3, W3a, W3u, W3, alpha3, alpha3p];
M2_func = Mach2_calc(gam,M2);
P2_it = P01/((M2_func*(Y_N+1))-Y_N);
P02_it = P2_it * M2_func;
Mw3_func = Machw3_calc (gam,Mw3);
M3_func = Mach3_calc (gam,M3);
P3_it = Pw2/((Mw3_func*(Y_R+1))-Y_R);
Pw3_it = P3_it * Mw3_func;
P03_it = P3_it * M3_func;
Kloss_stator = P02_it/P01;
Kloss_rotor = Pw3_it/Pw2;
end
T03 = T3*(1+0.5*(gam-1)*M3^2);
eta_TT = (1-(T03/T01))/(1-(P03_it/P01)^((gam-1)/gam));
end