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%% TAPERED INDUCER FLOW %
% Assumptions
% - Helical inducer, angular speed omega % - Constant tip radius r_T
% - Variable hub radius r_H % - N blades:
% -variable pitch P(z)
% -blade angle gamma (from axial direction) % - Incompressible, inviscid, adiabatic flow % - Uniform inlet flow (station 1)
% - Flow coefficient Phi
% - Radially uniform axial velocity w_cappuccio(z) % - 3D flow superposition:
% - fully-guided axisymmetric flow u_cappuccio with radially uniform
% velocity w_cappuccio(z)
% - 2D cross-sectional vorticity correction u_tilde, slip velocity stream % function psi(r,theta) %% GEOMETRICAL DATA clear all close all clc
global w_te_senza_bloccaggio w_te_con_bloccaggio fitting_v_s coeff_d_v_s_fittato omega r_T gamma_T ...
v_s dv_s v_te_ode v_2_ode II v_s_ODE dv_s_ODE v_te_ODE v_2_ODE%
p_v=0.0234.*10^5;%pressione vapore acqua 20°C [Pa]
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% Geometrical data DAPAMITO3
r_T=90.9*10^-3;% [m] raggio al tip
r_Hle=49.0*10^-3;% [m] raggio del mozzo in ingresso
r_Hte=68*10^-3;% [m] raggio del mozzo in uscita
c_a=0.07100;% [m] lunghezza assiale induttore
gamma_T_le=83.2*pi./180;% [rad]
%gamma_T_te=72.4.*pi./180;% [rad] solo per verifica
P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m]
N=3; % [-] blade number
r_H1=46.*10^-3; % non è più necessario definirlo a priori
theta_b_s=110.*pi/180; beta_blade=1.*pi./180;
rho=1000; % [kg/m^3] omega=3000.*2.*pi./60; %[rad/s] omega_D=omega; Phi=0.055; Phi_design=Phi; m=pi.*rho.*omega.*r_T.^3.*Phi; p_1=10.^5; %[Pa] inlet pressure
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% %Geometrical data Japanese 3-bladed inducer AIAA97-3026 %
% r_T=63.7*10^-3;% [m] raggio al tip
% r_Hle=19.11*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=31.85*10^-3;% [m] raggio del mozzo in uscita % c_a=0.0535;% [m] lunghezza assiale induttore
% gamma_T_le=82.75*pi./180;% [rad]
% gamma_T_te=80.75.*pi./180;% [rad] solo per verifica % P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m] % N=3; % [-] blade number % % r_H1=18.5.*10^-3; % theta_b_s=56.6.*pi/180; % beta_blade=1.*pi./180; %
% %% OPERATIONAL DATA JAPANESE 3-BLADED INDUCER AIAA97-3026 % % rho=1000; % [kg/m^3] % omega=7000.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi_japan_2_ALTA=(r_T.^2-r_Hle.^2)./r_T.^2; % Phi_design_japan=0.078; % Phi_design=Phi_design_japan.*Phi_japan_2_ALTA; % m=pi.*rho.*omega.*r_T.^3.*Phi_design;
% p_1=10.^5; %[Pa] inlet pressure
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%
% %Geometrical data Japanese 4-bladed inducer AIAA97-3026 %
% r_T=63.7*10^-3;% [m] raggio al tip
% r_Hle=19.11*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=31.85*10^-3;% [m] raggio del mozzo in uscita % c_a=0.046;% [m] lunghezza assiale induttore
% gamma_T_le=82.75*pi./180;% [rad]
% gamma_T_te=80.75.*pi./180;% [rad] solo per verifica % P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m] % N=4; % [-] blade number % % r_H1=18.5.*10^-3; % theta_b_s=56.36.*pi/180; % beta_blade=1.*pi./180; %
% % OPERATIONAL DATA JAPANESE 4-BLADED INDUCER AIAA97-3026 %
% rho=1000; % [kg/m^3] % omega=7000.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi_japan_2_ALTA=(r_T.^2-r_Hle.^2)./r_T.^2; % Phi_design_japan=0.0775; % Phi_design=Phi_design_japan.*Phi_japan_2_ALTA; % m=pi.*rho.*omega.*r_T.^3.*Phi_design;
% p_1=10.^5; %[Pa] inlet pressure
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% % %Geometrical data Japanese 3-bladed inducer ISROMAC 2002 FUJII %
% r_T=74.9*10^-3;% [m] raggio al tip
% r_Hle=19.11*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=31.85*10^-3;% [m] raggio del mozzo in uscita % c_a=0.0391;%0.0423 [m] lunghezza assiale induttore % gamma_T_le=82.5*pi./180;% [rad]
% gamma_T_te=81.*pi./180;% [rad] solo per verifica % P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m] % N=3; % [-] blade number % % r_H1=18.65.*10^-3; % theta_b_s=95.5.*pi/180; % beta_blade=1.*pi./180; %
% %% OPERATIONAL DATA JAPANESE 3-BLADED INDUCER ISROMAC 2002 FUJII % % rho=1000; % [kg/m^3] % omega=3000.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi_japan_2_ALTA=(r_T.^2-r_Hle.^2)./r_T.^2; % Phi_design_japan=0.0775; % Phi_design=Phi_design_japan.*Phi_japan_2_ALTA; % m=pi.*rho.*omega.*r_T.^3.*Phi_design;
% p_1=10.^5; %[Pa] inlet pressure
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% % %Geometrical data Japanese 3-bladed inducer FEDSM2005_77380 FUJII
% %
% r_T=87.*10^-3;% [m] raggio al tip
% r_Hle=24.969*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=40.020*10^-3;% [m] raggio del mozzo in uscita % c_a=0.055;% [m] lunghezza assiale induttore
% gamma_T_le=83.6*pi./180;% [rad]
% gamma_T_te=78.9.*pi./180;% [rad] solo per verifica % % solidity_@_TIP=2.1;
%
% P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m] % N=3; % [-] blade number
% r_H1=23.*10^-3;
% theta_b_s=60.*pi/180; % beta_blade=1.*pi./180; %
% %% OPERATIONAL DATA Japanese 3-bladed inducer FEDSM2005_77380 FUJII % % rho=1000; % [kg/m^3] % omega=1500.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi_japan_2_ALTA=(r_T.^2-r_Hle.^2)./r_T.^2; % Phi_design_japan=0.067; % Phi_design=Phi_design_japan.*Phi_japan_2_ALTA; % m=pi.*rho.*omega.*r_T.^3.*Phi_design;
% p_1=10.^5; %[Pa] inlet pressure
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % % Geometrical data MK1 % r_T=84*10^-3;% [m] raggio al tip
% r_Hle=36*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=58.25*10^-3;% [m] raggio del mozzo in uscita % c_a=0.060;% [m] lunghezza assiale induttore
% gamma_T_le=82.3.*pi./180;% [rad]
% gamma_T_te=atan(2.*r_T./(r_T+r_Hte).*tan(72.4.*pi./180));% [rad] solo per verifica
% P_Tle=2.*pi.*r_T./tan(gamma_T_le);% [m] % N=4; % [-] blade number % % r_H1=36.*10^-3; % theta_b_s=110.*pi/180; % beta_blade=1.*pi./180; % % % OPERATIONAL DATA MK1 % % rho=1000; % [kg/m^3] % omega=3000.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi=0.085; % Phi_design=Phi; % m=pi.*rho.*omega.*r_T.^3.*Phi; % p_1=10.^5; %[Pa] inlet pressure
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% % %Geometrical data FAST2
% r_T=41.1*10^-3;% [m] raggio al tip
% r_Hle=15*10^-3;% [m] raggio del mozzo in ingresso % r_Hte=28.3*10^-3;% [m] raggio del mozzo in uscita % c_a=0.03625;% [m] lunghezza assiale induttore
% gamma_T_le=82.6.*pi./180;% [rad]
% gamma_T_te=72.49.*pi./180;% [rad] solo per verifica % P_Tle=2.*pi.*r_T./tan(gamma_T_le);%[m] % N=2;% [-] blade number % load ('fast2_3000_rpm'); % % r_H1=38.*10^-3; % theta_b_s=110.*pi/180; % beta_blade=1.*pi./180; %
% % OPERATIONAL DATA FAST2 % % rho=1000; % [kg/m^3] % omega=3000.*2.*pi./60; %[rad/s] % omega_D=omega; % Phi=0.07; % Phi_design=Phi; % m=pi.*rho.*omega.*r_T.^3.*Phi; % p_1=10.^5; %[Pa] inlet pressure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % SUCTION PERFORMANCE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% sigma_b_D_max=(1- sin(gamma_T_le))./(1+sin(gamma_T_le)).*(Phi_design.^2/(1-r_Hle.^2./r_T.^2).^2+1); p_1_limite=sigma_b_D_max.*(0.5.*rho.*omega.^2.*r_T.^2)+p_v;% [Pa] %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% z=linspace(0,c_a,100); z_le=0; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %% FLOW BLOCKAGE
% Hub Geometry without Blockage
r_H=sqrt(r_T.^2-((1./((r_T.^2-r_Hte.^2))-...
1./((r_T.^2-r_Hle.^2))).*z./c_a+1./((r_T.^2-r_Hle.^2))).^(-1));
r_TT=r_T+0.*z;
% Pitch, Tip blade angle and blade cord
P_primo=P_Tle./c_a.*(((r_T.^2-r_Hle.^2))./((r_T.^2-r_Hte.^2))-1); P=P_Tle+P_primo.*z; %[m] P_te=P(end); gamma_T=atan(2.*pi.*r_T./P); figure('Name','Hub geometry') plot(z,r_H,z,r_TT); title('Hub geometry');
xlabel('z, m'); ylabel('r, m'); grid on; axis equal; ylim([0 1.1.*r_T]) format('long') figure('Name','Pitch') plot(z,P); title('Pitch'); xlabel('z, m'); ylabel('P, m');
figure('Name','Tip Blade Angle') plot(z,gamma_T.*180./pi);
title('Tip Blade Angle'); xlabel('z, m');
ylabel('\gamma_T, deg');
% calcolo del diffusion factor
w1_cappuccio=m./(pi.*rho.*(r_T.^2-r_Hle.^2));%NB senza bloccaggio
w2_cappuccio=m./(pi.*rho.*(r_T.^2-r_Hte.^2));%NB senza bloccaggio
P_te=P_Tle+P_primo.*c_a; r_M1=sqrt(0.5*(r_T.^2+r_Hle.^2)); r_M2=sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*c_a).*(r_T.^2-r_M1.^2)); v1=0; V1_primo=sqrt(w1_cappuccio.^2+omega.^2.*r_M1.^2); gamma_M2=atan(2.*pi.*r_M2./P_te); V2_primo=w2_cappuccio./cos(gamma_M2); v2=omega.*r_M2-w2_cappuccio.*tan(gamma_M2); v2_primo=-w2_cappuccio.*tan(gamma_M2); v1_primo=-omega.*r_M1; c_r_M=quad(@(x)sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).^(-0.5).*(r_T.^2-r_M1.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo).^ 2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a); sigma_r_M=quad(@(x)N./(2.*pi.*sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2))).*sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).^(-0.5).*(r_T.^2-r_M1.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo).^ 2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a);
D_r_M=(V1_primo-V2_primo)./V1_primo-omega.^2.*(r_M1.^2-r_M2.^2)./... (V1_primo.*(V1_primo+V2_primo))+(r_M2.*v2-r_M1.*v1)./(sigma_r_M.*(r_M1+r_M2).*V1_primo); [f_r_M]=diffusionfactor(D_r_M); B_te_r_M=1-1.3.*N.*c_r_M.*f_r_M./(pi.*r_M2.*cos(gamma_M2)); B_le=1;
B_te=B_te_r_M; %cambio di notazione per calcolare dr_H
disp('GEOMETRIA DI PROGETTO') disp(' ')
disp(sprintf('PHI di progetto [--]= %f',Phi_design)) disp(sprintf('Numero di Pale [--]= %f',N))
disp('---')
disp(sprintf('Bloccaggio a raggio medio in condizioni di disegno (B_te_r_M)= %f',B_te_r_M))
disp(sprintf('Strato limite di momento/corda (f_r_M)= %f',f_r_M)) disp(sprintf('Fattore di diffusione (D_r_M)= %f',D_r_M)) disp(' ') disp(' ') B=B_le+(B_te_r_M-B_le)./c_a.*z; %% HUB GEOMETRY r_H=sqrt(r_T.^2-1./B.*((1./((r_T.^2-r_Hte.^2).*B_te_r_M)-... 1./((r_T.^2-r_Hle.^2).*B_le)).*z./c_a+1./((r_T.^2-r_Hle.^2).*B_le)).^(-1)); dr_H=0.5.*r_H.^(-1).*((B_te-B_le)./c_a./B.^2.*((1./((r_T.^2-r_Hte.^2).*B_te)-1./... ((r_T.^2-r_Hle.^2).*B_le)).*z./c_a+1./((r_T.^2- r_Hle.^2).*B_le)).^(-1)+1./B.*((1./((r_T.^2-r_Hte.^2).*B_te)-1./... ((r_T.^2-r_Hle.^2).*B_le)).*z./c_a+1./((r_T.^2- r_Hle.^2).*B_le)).^(-2).*(1./((r_T.^2-r_Hte.^2).*B_te)-1./((r_T.^2-r_Hle.^2).*B_le))./c_a); r_TT=r_T+0.*z; %% Raccordo circonferenziale % z_r_ingresso=c_a-0.116; % r_raccordo=sqrt((0-z_r_ingresso).^2./(dr_H(1)).^2+(0-z_r_ingresso).^2); % r_ingresso=33.*10.^-3; % %r_centro_circonferenza=r_ingresso+r_raccordo; % r_centro_circonferenza=r_Hle+sqrt(r_raccordo.^2-(0-z_r_ingresso).^2); % z_ingresso=linspace(z_r_ingresso,0,100); % r_ingresso_vet=r_centro_circonferenza-sqrt(r_raccordo.^2-(z_ingresso-z_r_ingresso).^2);
z_r_ingresso=c_a-0.116; r_ingresso=33.*10.^-3;
Z_lineare=[z_r_ingresso.^3 z_r_ingresso.^2; 3.*z_r_ingresso.^2 2.*z_r_ingresso]; Termini_noto=[r_ingresso-r_Hle-dr_H(1).*z_r_ingresso; -dr_H(1)]; Coefficienti_cubica=Z_lineare\Termini_noto; z_ingresso=linspace(z_r_ingresso,0,100); r_ingresso_vet=Coefficienti_cubica(1).*z_ingresso.^3+Coefficienti_ cubica(2).*z_ingresso.^2+dr_H(1).*z_ingresso+r_Hle; % polinomio_interpolante=[Coefficienti_cubica(1) Coefficienti_cubica(2) dr_H(1) r_Hle-r_H1]; % radici_del_polinomio=roots(polinomio_interpolante); % intermedio=min(radici_del_polinomio(1),radici_del_polinomio(2)); % z_r_H1=min(intermedio,radici_del_polinomio(3)); z_r_H1=-P_Tle.*theta_b_s./(2.*pi); r_H1=Coefficienti_cubica(1).*z_r_H1.^3+Coefficienti_cubica(2).*z_r _H1.^2+dr_H(1).*z_r_H1+r_Hle; z_casing=linspace(z_r_ingresso,c_a,1000); clearance=0.5.*10.^-3; r_casing=r_T+clearance+0.*z_casing; z_spirale_logaritmica=linspace(z_r_H1,0,100); %r_spirale_logaritmica=(r_T-r_H1).*(z_spirale_logaritmica-z_r_H1)./(-z_r_H1)+r_H1; r_spirale_logaritmica=r_T.*exp(-2.*pi.*z_spirale_logaritmica./(P_Tle.*theta_b_s).*log(r_H1./r_T)); r_chiusura_pala=linspace(r_Hte,r_T,1000);
%% Pitch, Tip blade angle and blade cord
P_primo=P_Tle./c_a.*(((r_T.^2-r_Hle.^2).*B_le)./((r_T.^2-r_Hte.^2).*B_te_r_M)-1); P=P_Tle+P_primo.*z; %[m] P_te=P(end); gamma_T=atan(2.*pi.*r_T./P);
%% Axial Velocity con bloccaggio
w_cappuccio=m./(pi.*rho.*B.*(r_T.^2-r_H.^2)); w_le_cappuccio=w_cappuccio(1); w_te_cappuccio=w_cappuccio(end); dw_cappuccio=(w_te_cappuccio-w_le_cappuccio)./c_a; w_le_design=w_le_cappuccio;
%% Chord and solidity @ mean radius (con Bloccaggio)
r_M1=sqrt(0.5*(r_T.^2+r_Hle.^2));
r_M2_B=sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*c_a).*(r_T.^2-r_M1.^2));
c_r_M_B=quad(@(x)sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).^(-0.5).*(r_T.^2-r_M1.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo).^ 2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a); sigma_r_M_B=quad(@(x)N./(2.*pi.*sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2))).*sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).^(-0.5).*(r_T.^2-r_M1.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo).^ 2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_M1.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a); % spacing_zeta=(z(end)-z(1))/(length(z)-1); % d_theta=2.*pi./P-2.*pi.*z.*P_primo./P.^2; % % r_MEDIO=sqrt((r_T.^2+r_H.^2)./2); % dr_MEDIO=r_H.*dr_H./(2.*r_MEDIO); % % integrando_c_r_M_B=sqrt(1+(r_MEDIO.*d_theta).^2+dr_MEDIO.^2); % % [c_r_M_B]=Simpson(integrando_c_r_M_B,spacing_zeta); % % integrando_sigma_r_M_B=sqrt(1+(r_MEDIO.*d_theta).^2+dr_MEDIO.^2)./ (2.*pi.*r_MEDIO./N); % % [sigma_r_M_B]=Simpson(integrando_sigma_r_M_B,spacing_zeta);
% %% Chord and solidity @ TIP (con Bloccaggio)
c_r_T_B=quad(@(x)sqrt((r_T.*2*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c
_a);%corda valutata r=rT
sigma_r_T_B=quad(@(x)N./(2.*pi.*r_T).*sqrt((r_T.*2*pi./(P_Tle+P_pr imo.*x)).^2+1),z_le,c_a);%solidità valutata r=rT
% spacing_zeta=(z(end)-z(1))/(length(z)-1); % d_theta=2.*pi./P-2.*pi.*z.*P_primo./P.^2; % % integrando_c_r_T_B=sqrt(1+(r_T.*d_theta).^2); % % [c_r_T_B]=Simpson(integrando_c_r_T_B,spacing_zeta); % % integrando_sigma_r_T_B=sqrt(1+(r_T.*d_theta).^2)./(2.*pi.*r_T./N); % % [sigma_r_T_B]=Simpson(integrando_sigma_r_T_B,spacing_zeta); %
%c_r_T_B=quad(@(x)sqrt(1+(r_T.*(2.*pi./(P_Tle+P_primo.*x)-2.*pi.*x.*P_primo./(P_Tle+P_primo.*x).^2)).^2),z_le,c_a);%corda valutata r=rT
%% Chord and solidity @ HUB (con Bloccaggio)
r_H2=sqrt(r_T.^2-(r_T.^2-r_Hle.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*c_a)); c_r_H_B=quad(@(x)sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_Hle.^2)).^(-0.5).*(r_T.^2-r_Hle.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo). ^2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_Hle.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a);%corda valutata r=rHle sigma_r_H_B=quad(@(x)N./(2.*pi.*sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_Hle.^2))).*sqrt((0.5.*(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_Hle.^2)).^(-0.5).*(r_T.^2-r_Hle.^2).*(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x).^2.*P_primo). ^2+... (sqrt(r_T.^2-(P_Tle+P_primo.*z_le)./(P_Tle+P_primo.*x)... .*(r_T.^2-r_Hle.^2)).*2.*pi./(P_Tle+P_primo.*x)).^2+1),z_le,c_a);%solidità valutata r=rHle % spacing_zeta=(z(end)-z(1))/(length(z)-1); % d_theta=2.*pi./P-2.*pi.*z.*P_primo./P.^2; % % integrando_c_r_H_B=sqrt(1+(r_H.*d_theta).^2+dr_H.^2); % % [c_r_H_B]=Simpson(integrando_c_r_H_B,spacing_zeta); % % integrando_sigma_r_H_B=sqrt(1+(r_H.*d_theta).^2+dr_H.^2)./(2.*pi.* r_H./N); % % [sigma_r_H_B]=Simpson(integrando_sigma_r_H_B,spacing_zeta); % disp(sprintf('w_le_cappuccio= %f',w_le_cappuccio))
disp(sprintf('w_te_cappuccio (bloccato)= %f',w_te_cappuccio)) disp(' ')
disp(' ')
disp(sprintf('angolo di pala al TIP ingresso [deg]= %f',gamma_T(1)*180/pi))
disp(sprintf('angolo di pala al TIP uscita [deg]= %f',gamma_T(end)*180/pi))
disp(' ')
disp(sprintf('Raggio Hub le [mm]= %f',r_Hle.*10^3)) disp(sprintf('Raggio Hub te [mm]= %f',r_Hte.*10^3))
disp(sprintf('lunghezza assiale [m]= %f',c_a))
disp(sprintf('corda all'' HUB bloccaggio[m]= %f',c_r_H_B))
disp(sprintf('corda al RAGGIO MEDIO bloccaggio[m]= %f',c_r_M_B)) disp(sprintf('corda al TIP bloccaggio[m]= %f',c_r_T_B))
disp(' ')
disp(sprintf('P_p_r_i_m_o [--]= %f',P_primo)) disp(sprintf('P_T_l_e [mm]= %f',P_Tle.*10^3))
disp(' ')
disp(sprintf('solidità al''HUB [--]= %f',sigma_r_H_B))
disp(sprintf('solidità al RAGGIO MEDIO [--]= %f',sigma_r_M_B)) disp(sprintf('solidità al TIP [--]= %f',sigma_r_T_B))
disp(' ')
disp('---')
disp(' ')
disp(sprintf('Sigma breakdown max progetto (sigma_b_D_max)= %f',sigma_b_D_max))
disp(sprintf('Pressione in ingresso limite (p_1_limite) [bar]= %f',p_1_limite./10^5))
disp(' ')
figure('Name','Hub geometry Blockage')
plot(z,r_H,z,r_TT,z_ingresso,r_ingresso_vet,z_casing,r_casing,z_sp irale_logaritmica,r_spirale_logaritmica,c_a,r_chiusura_pala); title('Hub geometry Blockage');
xlabel('z, m'); ylabel('r, m'); grid on; axis square; axis equal; ylim([0 1.1.*r_T]) format('long') figure('Name','Pitch Blockage') plot(z,P); title('Pitch Blockage'); xlabel('z, m'); ylabel('P, m');
figure('Name','Tip Blade Angle Blockage') plot(z,gamma_T.*180./pi);
title('Tip Blade Angle Blockage'); xlabel('z, m');
ylabel('\gamma_T, deg');
MMM=[z.*1000; r_H.*1000]';
save dapamito_hub_geometry_1.out MMM -ASCII -tabs
NNN=[z_ingresso.*1000; r_ingresso_vet.*1000]'; save dapamito_hub_geometry_2.out NNN -ASCII -tabs
LLL=[z_spirale_logaritmica.*1000; r_spirale_logaritmica.*1000]'; save dapamito_hub_geometry_3.out LLL -ASCII -tabs
pause
%break % P_Tte=2.*pi.*r_T./tan(gamma_T_te); % gamma_T(end)=gamma_T_te; % P(end)=P_Tte; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
%ITERAZIONE SUL PHI
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% indice_phi=0; for Phi=0.01:0.005:0.12 w_2_rH22=[]; ss=[]; r_ODE_T=[]; ben=1; w_2_rH22(ben)=2.7;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%NNNBBB toll=0.0005; indice_phi=indice_phi+1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% % alfa/beta %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% alfa_alfa(indice_phi)=atan((r_T.^2-r_Hle.^2)./(Phi.*r_T.^2))-gamma_T_le; alfa_beta(indice_phi)=alfa_alfa(indice_phi)./(pi./2-gamma_T_le); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% PhiPhi(indice_phi)=Phi; m=pi.*rho.*omega.*r_T.^3.*Phi; portata_massica(indice_phi)=m; w_le_cappuccio=m./(pi.*rho.*(r_T.^2-r_Hle.^2)); w_te_senza_bloccaggio=m./(pi.*rho.*(r_T.^2-r_Hte.^2)); w_te_con_bloccaggio=m./(pi.*rho.*(r_T.^2-r_Hte.^2).*B(end)); r=linspace(r_H(end),r_T,100); spacing=(r(end)-r(1))/(length(r)-1);
%MK1 valutazione perdite circuito w1_inlet=0.06796867.*1500.*2.*pi/60.*(84*10^-3).^3./((84*10^-3).^2-(36*10^-3).^2); portata_inlet=rho.*w1_inlet.*pi.*((84*10^-3).^2-(36*10^-3).^2); DELTA_P_loss=0.160147.*rho.*(1500.*2.*pi/60.*84*10^-3).^2; F_LOSS=DELTA_P_loss./(0.5.*rho.*w1_inlet.^2);
%%MK1 Dp LOSS circuito con V_punto
F_LOSS_V_punto=0.160147.*rho./(pi.^2.*0.06796867.^2.*(84*10^-3).^4); PSI_DELTA_P_loss_loop_V_punto(indice_phi)=F_LOSS_V_punto.*pi.^2.*r _T.^4./rho.*Phi.^2; %MK1 Dp LOSS circuito DELTA_P_loss_loop(indice_phi)=F_LOSS.*(0.5.*rho.*w_le_cappuccio.^2 ); PSI_DELTA_P_loss_loop(indice_phi)=DELTA_P_loss_loop(indice_phi)./( rho.*omega.^2.*r_T.^2);
%%FIP162 Dp LOSS circuito con V_punto
F_LOSS_V_punto_FIP=0.125.*rho./(pi.^2.*0.067.^2.*(81*10^-3).^4); PSI_DELTA_P_loss_loop_V_punto_FIP(indice_phi)=F_LOSS_V_punto_FIP.* pi.^2.*r_T.^4./rho.*Phi.^2; % Hildebrand Solution %K=2.*(omega-2.*pi.*w1_cappuccio./P_Tle.*Phi./Phi_design);% DAPAMITO %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% K=2.*(omega-2.*pi.*w_te_senza_bloccaggio./P(end).*Phi./Phi_design);% DAPAMITO % B(end)=1; % P(end)=0.16517; % K=2.*omega.*(1-2.*pi.*Phi.*r_T.^3./(P(end).*(r_T^2-r_H(end)^2))); % VECCHIO %K=2.836882946468468e+002 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% L1=log(r_T./r_H(end)); L2=2.*pi./N; for ii=1:length(r) sommatoria_vsmn=0; sommatoria_derivata=0; for mm=30:-1:1 for nn=30:-1:1 sommatoria_vsmn=sommatoria_vsmn+((K.*r_H(end).^2.*(2.*mm./... ((2.*nn-1).*L1.^2))./(1+mm.^2.*pi.^2./(4.*L1.^2)).*... (1-(-1).^mm.*exp(2.*L1)))./(pi.^2.*(mm.^2./L1.^2+(2.*nn-1)...
.^2./L2.^2))).*2.*mm.*L2./((2.*nn-1).*L1).*cos(mm.*pi./L1.*... log(r(ii)./r_H(end)));%LUCIO sommatoria_derivata=sommatoria_derivata+((K.*r_H(end).^2.*... (2.*mm./((2.*nn-1).*L1.^2))./(1+mm.^2.*pi.^2./(4.*L1.^2))... .*(1-(-1).^mm.*exp(2.*L1)))./(pi.^2.*(mm.^2./L1.^2+... (2.*nn-1).^2./L2.^2))).*2.*mm.*L2./((2.*nn-1).*L1).*... -sin(mm.*pi./L1.*log(r(ii)./r_H(end))).*mm.*pi./L1./r(ii);%LUCIO end end vsmn_vet(ii)=N./(2.*pi.*r(ii)).*sommatoria_vsmn;%%LUCIO rvsmn_vet(ii)=N./(2.*pi).*sommatoria_vsmn;%%LUCIO dv_s_vett(ii) = -N./(2.*pi.*r(ii).^2).*sommatoria_vsmn+N./(2.*pi.*... r(ii)).*sommatoria_derivata; end
fitting_v_s= fit(r',vsmn_vet','poly3');%NB vuole colonne e il risultato è in colonna
v_s_fittato=fitting_v_s(r)';
coeff_d_v_s_fittato=[3*fitting_v_s.p1 2*fitting_v_s.p2 fitting_v_s.p3]; %coefficienti della derivata
d_v_s_fittato = polyval(coeff_d_v_s_fittato,r); % figure('Name','v_s') % plot(r,vsmn_vet,'p',r,v_s_fittato); % title('v_{slip}') % xlabel('r, m'); % ylabel('v_s, m/s'); % legend('v_s','v_s fittato') % % % % figure('Name','d_v_s') % plot(r,dv_s_vett,'p',r,d_v_s_fittato); % title('dvs') % xlabel('r, m'); % ylabel('dvs, m/s');
% legend('dvs derivata della serie','dvs derivata del polinomio FIT vs') v_2_average=omega.*r-w_te_cappuccio.*r./r_T.*tan(gamma_T(end))+vsmn_vet; % figure('Name','v_2_average') % hold on % plot(r,v_2_average,r,omega.*r,'o',r,-w_cappuccio(end).*r./r_T.*tan(gamma_T(end)),'p',r,vsmn_vet,'s'); % title('v_2 average') % xlabel('r, m'); % ylabel('v_2, m/s'); % legend('v2-average','omega*r','-w.*r./r_T.*tan(gamma_T)','v2-slip')
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%% ODE %%%%%%%%%%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %
% II=0;%inizializzazione indice intfunction % v_s_ODE=[]; % dv_s_ODE=[]; % v_te_ODE=[]; % v_2_ODE=[]; % v_s=[]; % dv_s=[]; % v_te_ode=[]; % v_2_ode=[]; % x=[]; % Y=[]; % % disp(' ')
% disp('ATTENDERE LA CONVERGENZA DELL''ODE') % contatore=0;
% disp(sprintf('iterazione numero= %f',contatore)) % % refine = 1; % % % options = odeset('RelTol',1e-7,'AbsTol',1e-7,'outputfcn',@intfunction,'refine',refine); % % [x,Y] = ode45(@pippo4_w_spalmata2_r_Hte,[r_Hte^2 r_T^2],[r_Hte^2 w_2_rH22],options);% % % options = odeset('RelTol',1e-10,'AbsTol',1e-10,'outputfcn',@intfunction,'refine',refine);
% [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],[r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit
% disp(' ');
% disp(sprintf('r_T= %f',r_T)) % disp(' ')
% r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben))) % disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben)))
%
% if ss(ben)<0 & abs(r_ODE_T(ben)-r_T)./r_T>toll % ben=ben+1;
% %w_2_rH22(ben)=2*w_2_rH22(ben-1); % w_2_rH22(ben)=w_2_rH22(ben-1)+2;
% II=0;%inizializzazione indice intfunction % v_s_ODE=[]; % dv_s_ODE=[]; % v_te_ODE=[]; % v_2_ODE=[]; % v_s=[]; % dv_s=[]; % v_te_ode=[]; % v_2_ode=[]; % x=[]; % Y=[];
%
% [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],...
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit % r_ODE_T(ben)=sqrt(Y(end,1));
% ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben))) % disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben)))
% else if abs(r_ODE_T(ben)-r_T)./r_T>toll % ben=ben+1;
% %w_2_rH22(ben)=0.5*w_2_rH22(ben-1); % w_2_rH22(ben)=w_2_rH22(ben-1)-2;
% II=0;%inizializzazione indice intfunction % v_s_ODE=[]; % dv_s_ODE=[]; % v_te_ODE=[]; % v_2_ODE=[]; % v_s=[]; % dv_s=[]; % v_te_ode=[]; % v_2_ode=[]; % x=[]; % Y=[]; % [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],...
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit
% r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben)))
% disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben))) % end
% end
% while ss(ben)==ss(ben-1) & abs(r_ODE_T(ben)-r_T)./r_T>toll % II=0;%inizializzazione indice intfunction
% v_s_ODE=[]; % dv_s_ODE=[]; % v_te_ODE=[]; % v_2_ODE=[]; % v_s=[]; % dv_s=[]; % v_te_ode=[]; % v_2_ode=[]; % x=[]; % Y=[]; % if r_ODE_T(ben)<r_T % ben=ben+1; % %w_2_rH22(ben)=2*w_2_rH22(ben-1); % w_2_rH22(ben)=w_2_rH22(ben-1)+2; % [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],...
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit
% r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben)))
% disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben))) % else ben=ben+1;
% %w_2_rH22(ben)=0.5*w_2_rH22(ben-1); % w_2_rH22(ben)=w_2_rH22(ben-1)-2;
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit % r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T); % disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben)))
% disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben))) % end
% end
% while abs(r_ODE_T(ben)-r_T)./r_T>toll
% II=0;%inizializzazione indice intfunction % v_s_ODE=[]; % dv_s_ODE=[]; % v_te_ODE=[]; % v_2_ODE=[]; % v_s=[]; % dv_s=[]; % v_te_ode=[]; % v_2_ode=[]; % x=[]; % Y=[]; % if ss(ben)~=ss(ben-1); % cambio=ben-1; % w_2_rH22_cambio=w_2_rH22(cambio); % ben=ben+1; % w_2_rH22(ben)=(w_2_rH22(ben-1)+w_2_rH22_cambio)/2; % [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],...
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit
% r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben)))
% disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben))) % else ben=ben+1;
% w_2_rH22(ben)=(w_2_rH22(ben-1)+w_2_rH22_cambio)/2; % [x,Y] = ode45(@DAPAMITO_ode,[r_Hte^2 r_T^2],...
% [r_Hte^2 w_2_rH22(ben)],options);% con derivata v_s fit
% r_ODE_T(ben)=sqrt(Y(end,1)); % ss(ben)=sign(r_ODE_T(ben)-r_T);
% disp(sprintf('valore iniziale w2rH22= %f',w_2_rH22(ben)))
% disp(sprintf('valore r_T ODE = %f',r_ODE_T(ben))) % end % end % % w_2_rH22_convergiuto(indice_phi)=w_2_rH22(end); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% % % disp('CONVERGENZA ODE') % disp(' ') % disp(sprintf('raggio al TIP (r_T)= %f',r_T))
% disp(sprintf('raggio al TIP ODE (r_T_te)= %f',sqrt(Y(end,1)))) % disp(' ')
%
% w_2_ODE=(Y(:,2)');%velocità assiale nella sezione 2
% v_te_ODE=v_te_ODE;%velocità azimutale uscita pale(te) con slip % v_2_ODE=v_2_ODE;%velocità tangenziale nella sezione 2
%
v_te_slip=omega.*r-w_te_senza_bloccaggio.*r./r_T.*tan(gamma_T(end))+v_s_fittato;
%
% fitting_w_2_ODE= fit(sqrt(x),w_2_ODE','poly4');%NB vuole colonne e il risultato è in colonna
% w_2_ODE_fittato=fitting_w_2_ODE(r)'; %
% fitting_v_2_ODE= fit(sqrt(x(2:end)),v_2_ODE','poly4');%NB vuole colonne e il risultato è in colonna
% v_2_ODE_fittato=fitting_v_2_ODE(r)'; % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % % r_ODE_equispacing2=linspace(sqrt(x(1)),sqrt(x(end)),1000); % portata_integrando_spaziato_ODE=2*pi.*w_2_ODE.*sqrt(x').*rho; % portata_integrando_spaziato_OK=interp1(sqrt(x),portata_integrando_ spaziato_ODE,r_ODE_equispacing2); % spacing_ODE2=(r_ODE_equispacing2(end)-r_ODE_equispacing2(1))/(length(r_ODE_equispacing2)-1); % % [portata_ODE]=Simpson(portata_integrando_spaziato_OK,spacing_ODE2) ; % % disp(sprintf('portata vera [kg/s]= %f',m))
% disp(sprintf('portata ODE (dall''integrazione della w2) [kg/s]= %f',portata_ODE)) %%%%%%%%%%%%%%%% MODELLO SEMPLIFICATO %%%%%%%%%%%%%%%%%%%%%%%% AA=2.*r.*(omega.*r.^2./r_T.*tan(gamma_T(end))+tan(gamma_T(end))./r _T.*rvsmn_vet)./(1+r.^2./r_T.^2.*(tan(gamma_T(end))).^2); BB=2.*r./(1+r.^2./r_T.^2.*(tan(gamma_T(end))).^2); [AAA]=Simpson(AA,spacing); [BBB]=Simpson(BB,spacing); BBB2=r_T.^2./(tan(gamma_T(end))).^2.*log((1+(tan(gamma_T(end))).^2 )./(1+r_Hte.^2./r_T.^2.*(tan(gamma_T(end))).^2)); c=((r_T.^2-r_Hle.^2).*w_le_cappuccio-AAA)./BBB; w_2=(omega.*r.^2./r_T.*tan(gamma_T(end))+tan(gamma_T(end))./r_T.*r vsmn_vet+c)./(1+r.^2./r_T.^2.*(tan(gamma_T(end))).^2); v_2=omega.*r-w_2.*r./r_T.*tan(gamma_T(end))+vsmn_vet; %w_te_su_tutto_raggio=m./(rho.*pi.*(r_T^2-r_Hte^2)); %v_2=omega.*r-w_te_su_tutto_raggio.*r./r_T.*tan(gamma_T(end))+vsmn_vet; portata_integrando=2*pi.*w_2.*r.*rho; [portata_MOD_SEMPLIFICATO]=Simpson(portata_integrando,spacing);
disp(' ')
disp('DISPONIBILI RISULTATI MODELLO SEMPLIFICATO')
disp('---')
disp(sprintf('Portata derivante integrazione w2 modello semplificato [kg/s]= %f',portata_MOD_SEMPLIFICATO)) disp(sprintf('Portata vera [kg/s]= %f',m))
disp('---')
%
% figure('Name','w_2 MODELLO SEMPLIFICATO') % hold on
% plot(r,w_2);
% title('w2 modello semplificato'); % xlabel('r, m');
% ylabel('w_2, m/s'); %
% figure('Name','v_2 MODELLO SEMPLIFICATO') % hold on
% plot(r,v_2);
% title('v2 modello semplificato'); % xlabel('r, m'); % ylabel('v_2, m/s'); % figure('Name','W2 ODE') % hold on % plot(sqrt(x),w_2_ODE,r,w_2_ODE_fittato,r,w_2); % title('W2 ODE') % xlabel('r, m'); % ylabel('w_2, m/s'); % legend('ODE','ODE w2 FIT','MOD') % figure('Name','v_te_ODE') % hold on % plot(sqrt(Y(2:end,1)),v_te_ODE); % title('v_t_e') % xlabel('r_te, m'); % ylabel('v_te, m/s'); % % v_2_mix=omega.*r-w_2_ODE_fittato.*r./r_T.*tan(gamma_T(end))+vsmn_vet; % % % figure('Name','v_2_ODE') % hold on % plot(sqrt(x(2:end)),v_2_ODE,r,v_2_ODE_fittato,r,v_2,sqrt(Y(2:end,1 )),v_te_ODE) % title('v2_{O_D_E}') % xlabel('r_2, m'); % ylabel('v2_{O_D_E}, m/s');
% legend('v2_{O_D_E}','v2 FIT','v_2 modello semplificato','v_t_e') % % % % figure('Name','legame RAGGI') % hold on % plot(sqrt(x),sqrt(x)./sqrt(Y(:,1))); % title('r_2/r_t_e') % xlabel('r_t_e, m'); % ylabel('r_2/r_t_e, []'); % axis([sqrt(x(1)) sqrt(x(end)) 0.8 1.3])
% box on
% Deviation Correction @ Design
r_M2=sqrt(0.5*(r_T.^2+r_Hte.^2)); gamma_M1=atan(r_M1./r_T.*tan(gamma_T(1))); gamma_M2=atan(r_M2./r_T.*tan(gamma_T(end))); m_c=0.23+0.1.*(gamma_M2.*180./pi./50); delta_zero=1.22.*m_c./sqrt(sigma_r_M_B).*(gamma_M1-gamma_M2); Beta_2_primo=atan((omega.*r-v_2)./w_2); v_2_delta_zero=omega.*r-w_2.*tan(Beta_2_primo+delta_zero); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ODE%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% % Beta_2_primo_ode=atan((omega.*r-v_2_ODE_fittato)./w_2_ODE_fittato); % v_2_delta_zero_ode=omega.*r-w_2_ODE_fittato.*tan(Beta_2_primo_ode+delta_zero); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ODE%%%%%%%%%%%%%%%%% %%%%%%%%%%%%% % % figure('Name','v_2_delta_zero') % hold on % plot(r,v_2_delta_zero,r,v_2_delta_zero_ode,r,v_2,r,v_2_ODE_fittato ); % title('v_2_delta_zero'); % xlabel('r, m'); % ylabel('v_2_delta_zero, m/s');
% legend('v_2_delta_zero MODELLO','v_2_delta_zero ODE','v_2 MODELLO','v_2 ODE')
%% PUMPING PERFORMANCE
%DELTA PRESSIONE TOTALE
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ODE %%%%%%%%%%%%%% % delta_p_t_ode=rho.*(omega.*r.*v_2_delta_zero_ode); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%OD E%%%%%%%%%%% delta_p_t=rho.*(omega.*r.*v_2_delta_zero); % figure('Name','delta_p_t')
% hold on % plot(r,delta_p_t); % title('delta_p_t [Pa]') % xlabel('r, m'); % ylabel('delta_p_t, Pa'); p_2=p_1+delta_p_t-0.5.*rho.*(v_2_delta_zero.^2+w_2.^2-w_le_cappuccio.^2); integrando_delta_p_t_medio=delta_p_t.*r.*w_2; [I_t_Simpson]=Simpson(integrando_delta_p_t_medio,spacing); delta_p_t_medio(indice_phi)=2.*pi.*rho./m.*I_t_Simpson; PSI_delta_p_t_medio(indice_phi)=delta_p_t_medio(indice_phi)./(rho. *omega.^2.*r_T.^2); delta_p_stat=p_2-p_1; integrando_delta_p_stat_medio=delta_p_stat.*r.*w_2; [I_stat_Simpson]=Simpson(integrando_delta_p_stat_medio,spacing); delta_p_stat_medio(indice_phi)=2.*pi.*rho./m.*I_stat_Simpson; PSI_delta_p_stat_medio(indice_phi)=delta_p_stat_medio(indice_phi). /(rho.*omega.^2.*r_T.^2); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ODE%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%ODE % p_2_ode=p_1+delta_p_t_ode- 0.5.*rho.*(v_2_delta_zero_ode.^2+w_2_ODE_fittato.^2-w_le_cappuccio.^2); % % integrando_delta_p_t_medio_ode=delta_p_t.*r.*w_2_ODE_fittato; % [I_t_Simpson]=Simpson(integrando_delta_p_t_medio_ode,spacing); % delta_p_t_medio_ode(indice_phi)=2.*pi.*rho./m.*I_t_Simpson; % PSI_delta_p_t_medio_ode(indice_phi)=delta_p_t_medio_ode(indice_phi )./(rho.*omega.^2.*r_T.^2); % % delta_p_stat_ode=p_2_ode-p_1; % % integrando_delta_p_stat_medio_ode=delta_p_stat_ode.*r.*w_2_ODE_fit tato; % [I_stat_Simpson]=Simpson(integrando_delta_p_stat_medio_ode,spacing ); % delta_p_stat_medio_ode(indice_phi)=2.*pi.*rho./m.*I_stat_Simpson; % PSI_delta_p_stat_medio_ode(indice_phi)=delta_p_stat_medio_ode(indi ce_phi)./(rho.*omega.^2.*r_T.^2); % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%ODE%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%ODE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%
% INTRODUZIONE DELLE PERDITE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% % Blade BL Losses omega_1_B=f_r_M.*(2.*sigma_r_M_B.*(cos(gamma_M1)).^2)./((cos(gamma _M2)).^3); r_M_medio=sqrt(0.5.*(r_M1.^2+r_M2.^2)); r_H_medio=sqrt(0.5.*(r_Hle.^2+r_Hte.^2)); w_1_D_medio=Phi_design.*omega_D.*r_T.^3./(r_T.^2-r_H_medio.^2); delta_p_t_PLD=omega_1_B.*0.5.*rho.*omega_D.^2.*r_M_medio.^2.*(1+(P hi_design.^2.*r_T.^6)./(r_M_medio.^2.*(r_T.^2-r_H_medio.^2).^2));
% Simplified Incidence Losses
delta_p_t_IL=0.5.*rho.*omega_D.^2.*r_M_medio.^2.*abs(Phi_design.^2 ./Phi.^2-1); % Total Losses delta_p_t_L(indice_phi)=delta_p_t_PLD+delta_p_t_IL; delta_PSI_p_t_L(indice_phi)=delta_p_t_L(indice_phi)./(rho.*omega.^ 2.*r_T.^2); PSI_delta_p_t_medio_L(indice_phi)=PSI_delta_p_t_medio(indice_phi)-delta_PSI_p_t_L(indice_phi); PSI_delta_p_stat_medio_L(indice_phi)=PSI_delta_p_stat_medio(indice _phi)-delta_PSI_p_t_L(indice_phi); % close all
% Perdite per attrito
w_1_medio(indice_phi)=m./(rho.*pi.*(r_T.^2-r_H_medio.^2)); V_1_primo(indice_phi)=sqrt(omega.^2.*r_M_medio.^2+w_1_medio(indice _phi).^2); f(indice_phi)=0.020; L=c_r_M_B; Perimetro=2.*pi./N.*(r_T+r_H_medio)+2.*(r_T-r_H_medio); D_H=4.*(pi.*(r_T.^2-r_H_medio.^2)./N)./Perimetro; % ni=0.894.*10.^-6; % Re(indice_phi)=D_H.*V_1_primo(indice_phi)./ni; % h_rettangolo=r_T-r_H_medio; b_rettangolo=pi./N.*(r_T+r_H_medio); h_b_ratio=h_rettangolo./b_rettangolo; a_b_ratio=r_T./r_H_medio; %f(indice_phi)=1.5.*(0.0032+0.221./(Re(indice_phi)).^0.237); %f(indice_phi)=0.309./(log(Re(indice_phi)./7)).^2; %f(indice_phi)=1./(2.*log(3.71.*D_H./0.00015)).^2; L_D_attrito=L./D_H; incidenza(indice_phi)=atan(omega.*r_M1./w_le_cappuccio)-atan(2.*pi.*r_M1./P(1));
L_D_eq_inc(indice_phi)=incidenza(indice_phi).*30.*2./pi; L_D_tot=L_D_attrito+L_D_eq_inc(indice_phi);%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 delta_p_friction(indice_phi)=f(indice_phi).*L_D_tot.*0.5.*rho.*V_1 _primo(indice_phi).^2; delta_PSI_friction(indice_phi)=delta_p_friction(indice_phi)./(rho. *omega.^2.*r_T.^2); PSI_delta_p_t_medio_friction(indice_phi)=PSI_delta_p_t_medio(indic e_phi)-delta_PSI_friction(indice_phi); PSI_delta_p_stat_medio_friction(indice_phi)=PSI_delta_p_stat_medio (indice_phi)-delta_PSI_friction(indice_phi); % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%ODE%%%%%%%%%% % PSI_delta_p_t_medio_friction_ode(indice_phi)=PSI_delta_p_t_medio_o de(indice_phi)-delta_PSI_friction(indice_phi); % PSI_delta_p_stat_medio_friction_ode(indice_phi)=PSI_delta_p_stat_m edio_ode(indice_phi)-delta_PSI_friction(indice_phi); % %%%%%%%%%%%%%%%%ODE%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% incidenza(indice_phi)=atan(omega.*r_M1./w_le_cappuccio)-atan(2.*pi.*r_M1./P(1)); L_D_eq_inc(indice_phi)=abs(incidenza(indice_phi).*50.*2./pi); figure(7) hold on plot(r,w_2); text(r(end),w_2(end),['\Phi: ',num2str(Phi)]) title('w_2 ') xlabel('r, m'); ylabel('w_2, m/s'); figure(8) hold on plot(r,v_2_delta_zero); text(r(end./2),v_2_delta_zero(end./2),['\Phi: ',num2str(Phi)]) title('v_2_{\delta^o} ') xlabel('r, m'); ylabel('v_2_{\delta^o} , m/s'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% Flow_exit_angle_deg_MOD=atan(v_2_delta_zero./w_2).*180./pi; Flow_exit_angle_deg_te=atan(v_te_slip./w_te_senza_bloccaggio).*180 ./pi; %Flow_exit_angle_deg_ODE=atan(v_2_delta_zero_ode./w_2_ODE_fittato) .*180./pi; figure(9) hold on plot(r,Flow_exit_angle_deg_MOD); text(r(end),Flow_exit_angle_deg_MOD(end),['\Phi: ',num2str(Phi)]) title('Flow exit angle 2 MOD')
xlabel('r, m');
ylabel('Flow exit angle 2 MOD, deg');
figure(10) hold on
plot(r,Flow_exit_angle_deg_te);
text(r(end),Flow_exit_angle_deg_te(end),['\Phi: ',num2str(Phi)]) title('Flow exit angle te')
xlabel('r, m');
ylabel('Flow exit angle te, deg'); % figure(11) % hold on % plot(r,Flow_exit_angle_deg_ODE); % text(r(end),Flow_exit_angle_deg_ODE(end),['\Phi: ',num2str(Phi)])
% title('Flow exit angle 2 ODE') % xlabel('r, m');
% ylabel('Flow exit angle 2 ODE, deg');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%% FLOW INCIDENCE %%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
P_primo_spir=P_primo.*1;% passo variabile
r_spir=linspace(r_H1,r_T,100); r_H1_vet=r_H1+(r_Hle-r_H1).*(r_spir-r_H1)./(r_T-r_H1);%ipotizzata variazione lineare %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% w1_le=Phi.*omega.*r_T^3./(r_T.^2-r_H1_vet.^2); z_le_spir=P_Tle./P_primo.*(exp(-P_primo_spir.*theta_b_s./(2.*pi).*log(r_spir/r_T)./log(r_H1_vet(1) ./r_T))-1)+... (r_T-r_spir).*tan(beta_blade);
incidence_spir=atan(omega.*r_spir./w1_le)-atan(2.*pi.*r_spir./(P_Tle+P_primo_spir.*z_le_spir)); alfa_beta_spir=incidence_spir./(pi/2-atan(2.*pi.*r_spir./(P_Tle+P_primo_spir.*z_le_spir))); incidence_spir_constant_pitch=atan(omega.*r_spir./w1_le)-atan(2.*pi.*r_spir./P_Tle); alfa_beta_spir_constant_pitch=incidence_spir_constant_pitch./(pi/2 -atan(2.*pi.*r_spir./P_Tle)); figure(11) hold on plot(r_spir,incidence_spir.*180./pi,'-',r_spir,incidence_spir_constant_pitch.*180./pi,'--'); text(r_spir(end),incidence_spir(end).*180./pi,['\Phi: ',num2str(Phi)])
title('INCIDENZA TRATTO SPIRALE LOG') xlabel('r [m]');
ylabel('i [deg]');
legend('variable pitch','constant pitch') grid on figure(12) hold on plot(r_spir,alfa_beta_spir,'-',r_spir,alfa_beta_spir_constant_pitch,'--'); text(r_spir(end),alfa_beta_spir(end),['\Phi: ',num2str(Phi)]) title('\alpha/\beta SPIRALE LOG')
xlabel('r [m]');
ylabel('\alpha/\beta [-]');
legend('variable pitch','constant pitch') grid on %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% end Power=PSI_delta_p_t_medio_friction.*PhiPhi; Ideal_Power=PSI_delta_p_t_medio.*PhiPhi;
figure('Name','PSI vs PHI senza perdite') hold on plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's'); title('\Psi vs \Phi') xlabel('\Phi'); ylabel('\Psi');
legend('PSI delta p_t medio','PSI delta p_{stat} medio') %%%%%%%%%%%%%%%%%%%%%%%%% PRSTAZIONI MK1 DAPAMITO %%%%%%%%%%%%%%%%%%% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%
PHI_1500_RENZO=[0.06796867 0.066566902 0.065233512 0.063797554 0.062088081 0.060515365... 0.05890846 0.05760926 0.055455323 0.054121934 0.052515029 0.050121766 0.048309724... 0.04663444 0.044788208 0.043147113 0.041061556 0.039796545 0.038668293 0.037095577... 0.035933135 0.034428798 0.032582567 0.031146609 0.029642272 0.028206314 0.026907114... 0.024958314 0.023043704 0.021470988 0.019932462 0.01877002 0.017675957 0.016616083... 0.015453641 0.013983494 0.012889431 0.011761178 0.01097482 0.010085894 0.008957642... 0.007966147 0.007043031 0.006359242 0.005367747 0.004444631 0.003555705 0.002700968... 0.001812042 0.001196632]; PSI_1500_RENZO=[0.160147 0.1657 0.170954 0.176685 0.183959 0.192966 0.200149 ... 0.206917 0.213631 0.216918 0.221228 0.227473 0.232163 0.236206 ... 0.239595 0.242213 0.243153 0.241711 0.244044 0.247096 0.248589 ... 0.253646 0.253858 0.259402 0.259524 0.259576 0.262029 0.265496 ... 0.26456 0.265924 0.2698 0.268925 0.270212 0.268105 0.270467 ... 0.271448 0.270082 0.273147 0.268082 0.266057 0.270015 0.265271 ... 0.264327 0.263922 0.262679 0.262617 0.261058 0.2571 0.264108 0.260372]; figure('Name','PSI vs PHI') hold on plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... PhiPhi,PSI_delta_p_t_medio_friction,'>') plot(PhiPhi,PSI_delta_p_stat_medio_friction,'--o','MarkerEdgeColor','k','MarkerFaceColor','c') plot(PhiPhi,delta_PSI_friction,'*',PhiPhi,1-PhiPhi.*tan(mean(gamma_T))) plot(PHI_1500_RENZO,PSI_1500_RENZO,'--p','MarkerEdgeColor','k','MarkerFaceColor','r') % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','b') % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','g') % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','r') % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'--o','MarkerEdgeColor','k','MarkerFaceColor','c'); % plot(PhiPhi,PSI_DELTA_P_loss_loop,'--o'); plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto,'--o','MarkerEdgeColor','k','MarkerFaceColor','g'); plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto_FIP,'--+') title('\Psi vs \Phi') xlabel('\Phi'); ylabel('\Psi');
legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
'ideal','MK1','perdite loop V_p_u_n_t_o MK1','perdite loop V_p_u_n_t_o FIP') % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%% PRESTAZIONI FAST2 %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% % % PHI_3000_FAST_2=MMM(1,:); % PSI_3000_FAST_2=MMM(2,:); % figure('Name','PSI vs PHI') % hold on % plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... % PhiPhi,PSI_delta_p_t_medio_friction,'>',PhiPhi,PSI_delta_p_stat_me dio_friction,'o',PhiPhi,delta_PSI_friction,'*',... % PhiPhi,1-PhiPhi.*tan(mean(gamma_T)),PHI_3000_FAST_2,PSI_3000_FAST_2,'p'); % % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','b') % % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','g') % % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'o','MarkerEdgeCol or','k','MarkerFaceColor','c'); % % title('\Psi vs \Phi') % xlabel('\Phi'); % ylabel('\Psi');
% legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
% 'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
% 'ideal','FAST2','PSI delta p_t medio ODE','PSI delta p_{stat} medio ODE',...
% 'PSI delta p_t medio friction ODE','PSI delta p_{stat} medio friction ODE')
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%
%%%% PRESTAZIONI JAPANESE 3_BLADED INDUCER AIAA97-3026 %%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% % % % PHI_3_JAPAN_2_ALTA=[0.057 0.062 0.069 0.076 0.078 0.083 0.089 0.0943].*Phi_japan_2_ALTA; % PSI_3_JAPAN=[0.182 0.175 0.157 0.140 0.135 0.122 0.102 0.082]; % % % figure('Name','PSI vs PHI') % hold on % plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... % PhiPhi,PSI_delta_p_t_medio_friction,'>') % plot(PhiPhi,PSI_delta_p_stat_medio_friction,'--o','MarkerEdgeColor','k','MarkerFaceColor','c') % plot(PhiPhi,delta_PSI_friction,'*',PhiPhi,1-PhiPhi.*tan(mean(gamma_T))) % plot(PHI_3_JAPAN_2_ALTA,PSI_3_JAPAN,'--p','MarkerEdgeColor','k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','b') % % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','g') % % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'--o','MarkerEdgeColor','k','MarkerFaceColor','c'); % % % plot(PhiPhi,PSI_DELTA_P_loss_loop,'--o'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto,'--o','MarkerEdgeColor','k','MarkerFaceColor','g'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto_FIP,'--+') % title('\Psi vs \Phi') % xlabel('\Phi'); % ylabel('\Psi');
% legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
% 'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
% 'ideal','JAPANESE 3 BLADED INDUCER','perdite loop V_p_u_n_t_o MK1','perdite loop V_p_u_n_t_o FIP')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
%%%%%%%%%%%% PRESTAZIONI JAPANESE 4_BLADED INDUCER AIAA97-3026 %%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% % % PHI_4_JAPAN_2_ALTA=[0.057 0.062 0.07 0.0783 0.081 0.0862 0.093 0.097].*Phi_japan_2_ALTA; % PSI_4_JAPAN=[0.182 0.170 0.149 0.123 0.115 0.100 0.075 0.060]; % % % figure('Name','PSI vs PHI')
% hold on % plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... % PhiPhi,PSI_delta_p_t_medio_friction,'>') % plot(PhiPhi,PSI_delta_p_stat_medio_friction,'--o','MarkerEdgeColor','k','MarkerFaceColor','c') % plot(PhiPhi,delta_PSI_friction,'*',PhiPhi,1-PhiPhi.*tan(mean(gamma_T))) % plot(PHI_4_JAPAN_2_ALTA,PSI_4_JAPAN,'--p','MarkerEdgeColor','k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','b') % % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','g') % % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'--o','MarkerEdgeColor','k','MarkerFaceColor','c'); % % % plot(PhiPhi,PSI_DELTA_P_loss_loop,'--o'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto,'--o','MarkerEdgeColor','k','MarkerFaceColor','g'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto_FIP,'--+') % title('\Psi vs \Phi') % xlabel('\Phi'); % ylabel('\Psi');
% legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
% 'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
% 'ideal','JAPANESE 4 BLADED INDUCER','perdite loop V_p_u_n_t_o MK1','perdite loop V_p_u_n_t_o FIP')
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
% %%%%%%% PRESTAZIONI JAPANESE 3_BLADED INDUCER ISROMAC 2002 FUJII %%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % % PHI_3_JAPAN_2_ALTA=[0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09].*Phi_japan_2_ALTA; % PSI_3_JAPAN=[0.28 0.26 0.22 0.19 0.17 0.13 0.10 0.07]; % % % figure('Name','PSI vs PHI') % hold on % plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... % PhiPhi,PSI_delta_p_t_medio_friction,'>') % plot(PhiPhi,PSI_delta_p_stat_medio_friction,'--o','MarkerEdgeColor','k','MarkerFaceColor','c') % plot(PhiPhi,delta_PSI_friction,'*',PhiPhi,1-PhiPhi.*tan(mean(gamma_T)))
% plot(PHI_3_JAPAN_2_ALTA,PSI_3_JAPAN,'--p','MarkerEdgeColor','k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','b') % % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','g') % % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'--o','MarkerEdgeColor','k','MarkerFaceColor','c'); % % % plot(PhiPhi,PSI_DELTA_P_loss_loop,'--o'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto,'--o','MarkerEdgeColor','k','MarkerFaceColor','g'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto_FIP,'--+') % title('\Psi vs \Phi') % xlabel('\Phi'); % ylabel('\Psi');
% legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
% 'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
% 'ideal','JAPANESE 3 BLADED INDUCER ISROMAC','perdite loop V_p_u_n_t_o MK1','perdite loop V_p_u_n_t_o FIP')
%%%%%%% PRESTAZIONI JAPANESE 3_BLADED INDUCER FEDSM2005_77380 FUJII %%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%% % % PHI_3_JAPAN_2_ALTA=[0.02 0.04 0.06 0.08 0.09].*Phi_japan_2_ALTA; % PSI_3_JAPAN_tot_stat=[0.33 0.26 0.20 0.14 0.12]; % velocita_assiale_ingresso=PHI_3_JAPAN_2_ALTA*omega.*r_T^3./(r_T.^2 -r_Hle.^2); % PSI_3_JAPAN=PSI_3_JAPAN_tot_stat+(0.5*velocita_assiale_ingresso.^2 /((omega.*r_T).^2)); % % % figure('Name','PSI vs PHI') % hold on % plot(PhiPhi,PSI_delta_p_t_medio,'p',PhiPhi,PSI_delta_p_stat_medio, 's',... % PhiPhi,PSI_delta_p_t_medio_friction,'>') % plot(PhiPhi,PSI_delta_p_stat_medio_friction,'--o','MarkerEdgeColor','k','MarkerFaceColor','c') % plot(PhiPhi,delta_PSI_friction,'*',PhiPhi,1-PhiPhi.*tan(mean(gamma_T))) % plot(PHI_3_JAPAN_2_ALTA,PSI_3_JAPAN,'--p','MarkerEdgeColor','k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_t_medio_ode,'p','MarkerEdgeColor','k','Mar kerFaceColor','b') % % plot(PhiPhi,PSI_delta_p_stat_medio_ode,'s','MarkerEdgeColor','k',' MarkerFaceColor','g')
% % plot(PhiPhi,PSI_delta_p_t_medio_friction_ode,'>','MarkerEdgeColor' ,'k','MarkerFaceColor','r') % % plot(PhiPhi,PSI_delta_p_stat_medio_friction_ode,'--o','MarkerEdgeColor','k','MarkerFaceColor','c'); % % % plot(PhiPhi,PSI_DELTA_P_loss_loop,'--o'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto,'--o','MarkerEdgeColor','k','MarkerFaceColor','g'); % plot(PhiPhi,PSI_DELTA_P_loss_loop_V_punto_FIP,'--+') % title('\Psi vs \Phi') % xlabel('\Phi'); % ylabel('\Psi');
% legend('PSI delta p_t medio MOD','PSI delta p_{stat} medio MOD',...
% 'PSI delta p_t medio friction MOD','PSI delta p_{stat} medio friction MOD','delta perdite',...
% 'ideal','JAPANESE 3 BLADED INDUCER FEDSM2005_77380 FUJII ','perdite loop V_p_u_n_t_o MK1','perdite loop V_p_u_n_t_o FIP')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
figure('Name','Nondimensional Power vs PHI senza perdite') hold on
plot(PhiPhi,Power,'p',PhiPhi,Ideal_Power,'o'); title('Nondimensional Power vs \Phi')
xlabel('\Phi');
ylabel('Nondimensional Power');
legend('Nondimensional Power','Nondimensional Ideal Power') figure('Name','Efficiency') hold on plot(PhiPhi,(Power./Ideal_Power),'p'); title('Efficiency vs \Phi') xlabel('\Phi'); ylabel('\eta'); w_1_NASA=omega.*r_T./tan(gamma_T_le+0.3.*(pi./2-gamma_T_le)); Phi_NASA=w_1_NASA.*(r_T.^2-r_Hle.^2)./(omega.*r_T.^3); Hydraulic_Power=PSI_delta_p_t_medio.*PhiPhi.*rho.*pi.*omega.^3.*r_ T.^5;
figure('Name','Hydraulic Power vs PHI senza perdite') hold on
plot(PhiPhi,Hydraulic_Power,'p'); title('Hydraulic Power vs \Phi') xlabel('\Phi'); ylabel('Hydraulic Power'); legend('Hydraulic Power') figure('Name','Incidence Angle') hold on plot(PhiPhi,alfa_alfa.*180./pi,'--p'); alfa_alfa_design=interp1(PhiPhi,alfa_alfa,Phi_design); plot(Phi_design,alfa_alfa_design.*180./pi,'p','MarkerEdgeColor','k ','MarkerFaceColor','r');
title('Incidence Angle @ TIP') xlabel('\Phi');
ylabel('\alpha @ Tip'); grid on figure('Name','alfa/beta') hold on plot(PhiPhi,alfa_beta,'--p'); alfa_beta_design=interp1(PhiPhi,alfa_beta,Phi_design); plot(Phi_design,alfa_beta_design,'p','MarkerEdgeColor','k','Marker FaceColor','g'); title('\alpha/\beta @ TIP') xlabel('\Phi'); ylabel('\alpha /\beta'); grid on disp(' ') disp(' ') disp('---')
disp(sprintf('Angolo di Incidenza a Disegno [deg]= %f',alfa_alfa_design.*180./pi)) disp(sprintf('ALPHA/BETA [--]= %f',alfa_beta_design)) disp('---') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% %%%% FLOW INCIDENCE %%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%% % r_H1_mm=55; % theta_b_s_DEG=110; % beta_blade_DEG=1; % %
% % r_H1_mm=input('INSERIRE IL VALORE DEL RAGGIO DEL MOZZO ALLA SEZIONE 1 in [mm]');
% r_H1=r_H1_mm.*10^-3;
% % theta_b_s_DEG=input('INSERIRE IL VALORE DELL''ANGOLO DI BACKSWEEP [DEG]');
% theta_b_s=theta_b_s_DEG.*pi/180;
% % beta_blade_DEG=input('INSERIRE IL VALORE DEL BLADE TAPERED MERIDIONAL HALF ANGLE (BETA_BLADE) [DEG]');
% beta_blade=beta_blade_DEG.*pi./180; P_primo_spir=P_primo.*1; %Phi_design=0.060; r_spir=linspace(r_H1,r_T,100); r_H1=r_H1+(r_Hle-r_H1).*(r_spir-r_H1)./(r_T-r_H1);%ipotizzata variazione lineare w1_design=Phi_design.*omega.*r_T^3./(r_T.^2-r_H1.^2); z_le_spir=P_Tle./P_primo.*(exp(-P_primo_spir.*theta_b_s./(2.*pi).*log(r_spir/r_T)./log(r_H1(1)./r_ T))-1)+... (r_T-r_spir).*tan(beta_blade);
incidence_spir=atan(omega.*r_spir./w1_design)-atan(2.*pi.*r_spir./(P_Tle+P_primo_spir.*z_le_spir)); alfa_beta_spir=incidence_spir./(pi/2-atan(2.*pi.*r_spir./(P_Tle+P_primo_spir.*z_le_spir))); incidence_spir_constant_pitch=atan(omega.*r_spir./w1_design)-atan(2.*pi.*r_spir./P_Tle); alfa_beta_spir_constant_pitch=incidence_spir_constant_pitch./(pi/2 -atan(2.*pi.*r_spir./P_Tle)); figure(11) hold on plot(r_spir,incidence_spir.*180./pi,'r-',r_spir,incidence_spir_constant_pitch.*180./pi,'r--'); title('INCIDENZA TRATTO SPIRALE LOG')
xlabel('r [m]'); ylabel('i [deg]');
legend('variable pitch','constant pitch') grid on figure(12) hold on plot(r_spir,alfa_beta_spir,'r-',r_spir,alfa_beta_spir_constant_pitch,'r--'); title('\alpha/\beta SPIRALE LOG')
xlabel('r [m]');
ylabel('\alpha/\beta [-]');
legend('variable pitch','constant pitch') grid on r_le_alfa=linspace(r_Hle,r_T,100); % alfa_r_le=atan(omega.*r_le_alfa./w1_design)-atan(2.*pi.*r_le_alfa./(0.056)); alfa_r_le=atan((r_T.^2- r_Hle.^2).*r_le_alfa./(Phi_design.*r_T.^3))-atan(r_le_alfa./r_T.*tan(gamma_T_le)); figure('Name','INCIDENZA AL LE') hold on plot(r_le_alfa,alfa_r_le.*180./pi,'g'); title('\alpha_L_E') xlabel('r [m]'); ylabel('\alpha_L_E [deg]'); legend('section le z=0') grid on %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%
