Contents

%Rankine Cycle with Supercritical pressure%
% In water, the critical point occurs at 647.096 K (373.946 °C; 705.103 °F)
% and 22.064 megapascals (3,200.1 psi; 217.75 atm).[2]

Given

clear
T_H = (1000 - 32) * (5/9) ;   % Boiler temperature (1000 F)
W_dot_net = 512 * 10^6;       % Plant Outpu (512 MW)
T_C = 25 ;        %Condenser temperature (25 C)

Required

Find the optimum Boiler pressure to increase the plant efficiency subjected to the design constraint of Steam quality at the Turbine exit pressure > 0.85. Calculate the required mass flow rate Plot this parameteric study on appropriate axis.

Solution

% State 1, Boiler exit/Turbine inlet
for i = 1:200
    p1(:,i) = 5 + i*5; %bar input variable
    T1 = T_H;
    h1 = XSteam('h_pT', p1(i), T1);    %kj/kg
    s1 = XSteam('s_pT', p1(i), T1);    %kj/kg
    % State 2, Turbine exit/Condenser inlet
    s2 = s1;
    p2 = XSteam('psat_T', T_C);
    h2 = XSteam('h_ps', p2, s2);    %kj/kg
    x2(:,i) = XSteam('x_ps', p2, s2);    %kj/kg
    % State 3, Condenser exit/Pump inlet
    x3 = 0;
    T3 = T_C;
    s3 = XSteam('sL_T',T3);    %kj/kg
    h3 = XSteam('hL_T', T3);    %kj/kg
    p3 = XSteam('psat_T', T3);    %convert Pascals to bar
    % State 4, Pump exit/Boiler inlet
    s4 = s3;
    p4 = p1(i);
    h4 = XSteam('h_ps', p4, s4);    %kj/kg
    T4 = XSteam('T_ps', p4, s4);    %C

    % Component energy balances”
    w_t = (h1-h2);           %turbine
    q_cond = (h2-h3);        %condenser
    w_p = (h4-h3);           %pump
    q_b = (h1-h4);           %boiler

    % check on solution using an overall energy balance
    %check_1 = (W_dot_t\m_dot)+(Q_dot_cond\m_dot)-(W_dot_p\m_dot)-(Q_dot_b\m_dot);
    w_net = w_t - w_p; % kJ/kg net specific work or simply net power per mass
    m_dot(:,i) = W_dot_net/w_net *2.2*60*60/1000;% mass flow rate in lbm/hr
    eta_Rankine(:,i) = w_net / q_b; %efficiency
    heat_rate_BtupkWhr = 3412./eta_Rankine ; %heat rate, in Btu/kW-hr
    eta_max = 1- ((T_C+273) /(T_H+273)); %maximum possible efficiency
end

figure
hold on
yyaxis left
title('Effect of Boiler Pressure')
plot(p1, eta_Rankine);
xlabel('Boiler Pressure (bar)')
ylabel('Efficiency [-]')

yyaxis right
plot(p1, x2);
xlabel('Boiler Pressure (bar)')
ylabel('Turbine Exit X [-]')
hold off

figure
plot(p1, m_dot);
title('For Power Output 512 MW')
xlabel('Boiler Pressure (bar)')
ylabel('Mass Flowrate [lbm/hr]')

Published with MATLAB® R2021a