The code does not converge

%% Input data
MM = 23.546; % molar mass, g/mol
gamma = 1.2775;
T0t = 600 + 273.15; % inlet total temperature, kelvin
m_flow = 0.65; % mass flow, kg/s
betaTS = 2.5; % total to static expansion ratio available
P4 = 1*101325; % outlet pressure, Pa
P0t = betaTS*P4;
R = 8.314/(MM*10^-3); % specifc gas constant
Cp = R/(gamma - 1); % specific heat at constant pressure, J/kg*K
viscosity = 1.8e-5; % viscosity of the fluid assumed equal to the one of air
%% Starting design point
% Balje Chart 
etaTT = 0.9; % total to total efficiency
omega_s = 0.5; % specific speed
D_s = 4; % specific diameter
% Chen-Baines (for eta_TT = 0.9)
flow_coeff = 0.215; % flow coefficient
work_coeff = 0.94; % work coefficient
%% Optimal work computation
T2t = T0t;
L_is = Cp*T0t*(1-betaTS^((1-gamma)/gamma)); % isentropic work, J/kg
P3t_is = P4; % isentropic total pressure at rotor outlet, Pa
T3t_is = T2t - L_is/Cp; % isentropic total temperature at rotor outlet, kelvin
rho3t_is = P3t_is/(R*T3t_is); % isentropic total density at rotor outlet, kg/
err_rho3 = 1;
rho3 = rho3t_is;  
while abs(err_rho3) > 1e-6
    Q_out = m_flow/rho3; % volumetric flow rate at rotor outlet
    omega = ((omega_s*L_is^0.75)/Q_out^0.5)*60/(2*pi); % rotor rotational speed, rpm
    D2 = (D_s*Q_out^0.5)/L_is^0.25; % rotor inlet diameter
    U2 = omega*(2*pi/60)*D2/2; % rotor inlet peripheral speed
    V3_tangential = 0; % rotor outlet tangential absolute velocity
    L_eul = etaTT*L_is; % Euler work isentropic
    V2_tangential = L_eul/U2;
    V3_axial = flow_coeff*U2;
    % Rotor outlet design
    R3_hub = 0.09; % DESIGN CHOICE (hub radius, m)
    equation = @(rho) rho*V3_axial*pi*((R3_hub^2+(2*(m_flow/(rho*pi*omega*(2*pi/60)))^2)^(1/3))-R3_hub^2)-m_flow;
    rho3_new = fsolve(equation, rho3);
    err_rho3 = rho3_new - rho3;
    rho3 = rho3 + 0.1 *(rho3_new - rho3);        
end

Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


Equation solved.

fsolve completed because the vector of function values is near zero
as measured by the value of the function tolerance, and
the problem appears regular as measured by the gradient.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.


No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
value of the function tolerance.

[Voss]

Looks like head_is is still undefined (see above).

[Les Beckham]

The code you posted doesn't run at all (see error message below) so it will be difficult for anyone to help you figure out why it isn't converging. Please provide all data necessary to allow it to run. Also, please format the code as code (select all of the code and click the left hand button in the CODE section of the toolstrip).

%% Input data
MM = 23.546; % molar mass, g/mol
gamma = 1.2775;
T0t = 600 + 273.15; % inlet total temperature, kelvin
m_flow = 0.65; % mass flow, kg/s
betaTS = 2.5; % total to static expansion ratio available
P4 = 1*101325; % outlet pressure, Pa
P0t = betaTS*P4;
R = 8.314/(MM*10^-3); % specifc gas constant
Cp = R/(gamma - 1); % specific heat at constant pressure, J/kg*K
viscosity = 1.8e-5; % viscosity of the fluid assumed equal to the one of air
%% Starting design point
% Balje Chart 
etaTT = 0.9; % total to total efficiency
omega_s = 0.5; % specific speed
D_s = 4; % specific diameter
% Chen-Baines (for eta_TT = 0.9)
flow_coeff = 0.215; % flow coefficient
work_coeff = 0.94; % work coefficient
%% Optimal work computation
T2t = T0t;
L_is = Cp*T0t*(1-betaTS^((1-gamma)/gamma)); % isentropic work, J/kg
P3t_is = P4; % isentropic total pressure at rotor outlet, Pa
T3t_is = T2t - L_is/Cp; % isentropic total temperature at rotor outlet, kelvin
rho3t_is = P3t_is/(R*T3t_is); % isentropic total density at rotor outlet, kg/
err_rho3 = 1;
rho3 = rho3t_is;  
    while abs(err_rho3) > 1e-5
        Q_out = m_flow/rho3; % volumetric flow rate at rotor outlet
        omega = ((omega_s*head_is^0.75)/Q_out^0.5)*60/(2*pi); % rotor rotational speed, rpm
        D2 = (D_s*Q_out^0.5)/head_is^0.25; % rotor inlet diameter
        U2 = omega*(2*pi/60)*D2/2; % rotor inlet peripheral speed
        V3_tangential = 0; % rotor outlet tangential absolute velocity
        L_eul = etaTT*L_is; % Euler work isentropic
        V2_tangential = L_eul/U2;
        V3_axial = flow_coeff*U2;
% Rotor outlet design
        R3_hub = 0.09; % DESIGN CHOICE (hub radius, m)
        equation = @(rho) rho*V3_axial*pi*((R3_hub^2+(2*(m_flow/(rho*pi*omega*(2*pi/60)))^2)^(1/3))-R3_hub^2)-m_flow;
        rho3_new = fsolve(equation, rho3);
        err_rho3 = rho3_new - rho3;
        rho3 = rho3 + 0.1 * (rho3_new - rho3);        
    end

Unrecognized function or variable 'head_is'.

[David Ricardo Macedo Ramos De Afonso Matias]

I'm sorry about that, the code should run now.

Answer 1

[Torsten]

I seems your function does not vary much with rho. The evaluation cannot find a value for rho for which the function has a zero.

rho=0.01:0.1:200;
res = arrayfun(@(i)fun(rho(i)),1:numel(rho));
plot(rho,res)

function res = fun(rho3)
%% Input data
MM = 23.546; % molar mass, g/mol
gamma = 1.2775;
T0t = 600 + 273.15; % inlet total temperature, kelvin
m_flow = 0.65; % mass flow, kg/s
betaTS = 2.5; % total to static expansion ratio available
P4 = 1*101325; % outlet pressure, Pa
P0t = betaTS*P4;
R = 8.314/(MM*10^-3); % specifc gas constant
Cp = R/(gamma - 1); % specific heat at constant pressure, J/kg*K
viscosity = 1.8e-5; % viscosity of the fluid assumed equal to the one of air
%% Starting design point
% Balje Chart 
etaTT = 0.9; % total to total efficiency
omega_s = 0.5; % specific speed
D_s = 4; % specific diameter
% Chen-Baines (for eta_TT = 0.9)
flow_coeff = 0.215; % flow coefficient
work_coeff = 0.94; % work coefficient
%% Optimal work computation
T2t = T0t;
L_is = Cp*T0t*(1-betaTS^((1-gamma)/gamma)); % isentropic work, J/kg
P3t_is = P4; % isentropic total pressure at rotor outlet, Pa
T3t_is = T2t - L_is/Cp; % isentropic total temperature at rotor outlet, kelvin


    Q_out = m_flow/rho3; % volumetric flow rate at rotor outlet
    omega = ((omega_s*L_is^0.75)/Q_out^0.5)*60/(2*pi); % rotor rotational speed, rpm
    D2 = (D_s*Q_out^0.5)/L_is^0.25; % rotor inlet diameter
    U2 = omega*(2*pi/60)*D2/2; % rotor inlet peripheral speed
    V3_tangential = 0; % rotor outlet tangential absolute velocity
    L_eul = etaTT*L_is; % Euler work isentropic
    V2_tangential = L_eul/U2;
    V3_axial = flow_coeff*U2;
    % Rotor outlet design
    R3_hub = 0.09; % DESIGN CHOICE (hub radius, m)
    res=rho3*V3_axial*pi*((R3_hub^2+(2*(m_flow/(rho3*pi*omega*(2*pi/60)))^2)^(1/3))-R3_hub^2)-m_flow;
       
end