From 30d2a1722649e82a4ad5bd7c8a99b271b188f22d Mon Sep 17 00:00:00 2001 From: Danilo Ciliberti Date: Sat, 26 Aug 2023 10:55:02 +0200 Subject: [PATCH] First upload --- .gitignore | 2 + drying_example.m | 73 ++++++++++++++++++++++++++++++ drying_example.mlx | Bin 0 -> 73076 bytes drying_example.pdf | Bin 0 -> 312040 bytes label_v5.mltbx | Bin 0 -> 609253 bytes mollier.m | 108 +++++++++++++++++++++++++++++++++++++++++++++ mollier_script.m | 40 +++++++++++++++++ scheme.jpg | Bin 0 -> 43736 bytes 8 files changed, 223 insertions(+) create mode 100644 .gitignore create mode 100644 drying_example.m create mode 100644 drying_example.mlx create mode 100644 drying_example.pdf create mode 100644 label_v5.mltbx create mode 100644 mollier.m create mode 100644 mollier_script.m create mode 100644 scheme.jpg diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..b436803 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +*.asv +*robosan* \ No newline at end of file diff --git a/drying_example.m b/drying_example.m new file mode 100644 index 0000000..111a1f3 --- /dev/null +++ b/drying_example.m @@ -0,0 +1,73 @@ +close all; clearvars; clc + +% Input data +p_amb = 101325; % ambient pressure in Pascal +T_amb = 22; % temperature in Celsius of ambient air +phi_amb = 0.6; % relative humidity (0.05 - 1.00) of ambient air +T_prh = 72; % temperature in Celsius of preheated air + +% Water vapor pressure in Pascal +vaporPressure = @(T) 0.61121 * exp((18.678 - T/234.5) .* T./(257.14 + T)) * 1000; +pv_amb = vaporPressure(T_amb); % water vapor pressure of ambient air +pv_prh = vaporPressure(T_prh); % water vapor pressure of preheated air + +% Air humidity in kg water per kg dry air +Y = 18.01/28.96 * phi_amb * pv_amb ./ (p_amb - phi_amb * pv_amb); + +% Relative humidity of preheated air +phi_prh = p_amb / pv_prh * Y / (18.01/28.96 + Y); + +% Air and water vapor constants +Cpg = 1000; % air specific heat at constant pressure in J / (kg K) +Cpv = 1860; % water vapor specific heat at constant pressure in J / (kg K) +Cpl = 4200; % liquid water specific heat at constant pressure in J / (kg K) +delta_hv_0 = 2500900; % water vaporization enthalpy at 0°C in J/kg + +% Enthalpy of preheated air +h = Cpg * T_prh + Y * (delta_hv_0 + Cpv*T_prh); + +% Saturation coordinates +Y_star_fun = @(T) 18.01/28.96 * vaporPressure(T) ./ (p_amb - vaporPressure(T)); +h_star_fun = @(T) Cpg * T + Y_star_fun(T) * (delta_hv_0 + Cpv*T); +adb_line_fun = @(T) (h_star_fun(T) - h) / (Y_star_fun(T) - Y) - Cpl*T; + +T_star = fzero(adb_line_fun,T_prh); +Y_star = Y_star_fun(T_star); +h_star = h_star_fun(T_star); + +% Drying rate +alpha = 20; % heat transfer coefficient in W / (m2 K) +delta_hv = 2430300; % vaporization enthalpy at T* in J/kg +Mdot = alpha * (T_prh - T_star) / delta_hv * 3600; % drying rate in kg / (m2 h) + +%% Plot of the Mollier diagram +temp = [-20, 80]; +mollier([phi_amb, phi_prh, 1.0], [40, 80, 120]*1000, temp, p_amb) + +% Add annotations +hold on +ax = plot([Y, Y]*1000, [temp(1), T_amb], 'k--'); +label(ax,'Y', 'location','left') + +ax = plot([Y_star, Y_star]*1000, [temp(1), T_star], 'k--'); +label(ax,'Y^*', 'location','left') + +ax = plot([0, Y]*1000, [T_amb, T_amb], 'k'); +label(ax,'T_{amb}', 'location','top') + +ax = plot([0, Y]*1000, [T_prh, T_prh], 'k'); +label(ax,'T_{preheat}', 'location','top') + +ax = plot([Y, Y_star]*1000, [T_prh, T_star], 'k', 'LineWidth',0.1); +label(ax,'adiabatic saturation line', 'location','left','slope') + +ax = plot([0, Y_star]*1000, [T_star, T_star], 'k'); +label(ax,'T^*', 'location','top') + +quiver(0,T_amb,Y*1000,0,'off','LineWidth',2) +quiver(Y*1000,T_amb,0,T_prh-T_amb,'off','LineWidth',2) +quiver(Y*1000,T_prh,(Y_star-Y)*1000,T_star-T_prh,'off','LineWidth',2); +quiver(Y_star*1000,T_star,-Y_star*1000,0,'off','LineWidth',2) + +hold off +xlabel('Humidity, g H_2O / kg dry air') \ No newline at end of file diff --git a/drying_example.mlx b/drying_example.mlx new file mode 100644 index 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PHI is a numeric array of relative +% humidities (accept values between 0.01 and 1.00) and ENT is a numeric +% array of specific entalpy in J/kg. The last PHI value will always be 1.0, +% independtly from the user input. +% +% MOLLIER([PHI],[ENT],[TEM]) draws the Mollier chart as the previous case +% with the prescribed range of temperature TEM, defined as [t_initial, +% t_final] in Celsius degrees. +% +% MOLLIER([PHI],[ENT],[TEM],P) also prescribes the ambient pressure with +% the scalar P in Pascal. +% +% MOLLIER([PHI],[ENT],[TEM],P,CPG,CPV,DELTA_HV_0) adds custom values for +% the constant pressure spefici heat for the gas CPG and the vapor CPV in +% J/(kg K), as well as the liquid vaporization enthalpy at 0°C in J/kg. + +% Check if the 'label' community package has been installed +addons = matlab.addons.installedAddons; +if ~any(strcmp("label", addons.Name)) + error(['LABEL add-on not found. Please retrieve it from: ',... + 'https://www.mathworks.com/matlabcentral/fileexchange/47421-label']) +end + +narginchk(0,7) + +% Demo mode +relHum = [0.05, 0.2, 0.6, 1.0]; % relative humidity array +enthalpy = [40000, 80000, 120000]; % specific enthalpy array, J/kg +temp = [-20,80]; % temperature array, Celsius +pamb = 101325; % ambient pressure, Pa +Cpg = 1000; % air specific heat at constant pressure, J / (kg K) +Cpv = 1860; % water vapor specific heat at constant pressure, J / (kg K) +delta_hv_0 = 2500900; % water vaporization enthalpy at 0°C, J/kg + +if nargin > 0 + relHum = varargin{1}; + enthalpy = varargin{2}; + + % Check limits for relative humidity + if min(relHum) < 0 || max(relHum) > 1 + error('Relative humidity values are out of bounds [0, 1]') + end + + % The last value of relative humidity must be 1.0 + if relHum(end) < 1 + relHum = [relHum, 1.0]; + end +end + +if nargin > 2 + temp = varargin{3}; +end + +if nargin > 3 + pamb = varargin{4}; +end + +if nargin > 4 + Cpg = varargin{5}; + Cpv = varargin{6}; + delta_hv_0 = varargin{7}; +end + +% Water vapor pressure in Pascal +T = temp(1):temp(2); +pv_star = (0.61121 * exp((18.678 - T/234.5) .* T./(257.14 + T))) * 1000; + +% Check if vapor pressure gets larger than ambient pressure +if any(pv_star > pamb) + warning(['Some values of the vapor pressure are larger than the ',... + 'ambient pressure. Please check the temperature interval as ',... + 'well as the ambient pressure, together with the gas properties.']) +end + +% Air humidity in kg water per kg dry air +figure +xlim([0,40]) +hold on +for phi = relHum + Y_phi = 18.01/28.96 * phi * pv_star ./ (pamb - phi * pv_star); + + ax = plot(Y_phi*1000,T,'k'); + label(ax,['\phi = ', num2str(phi,'%.2f')],'location','right','slope') +end + +for h = enthalpy + Y_h = (h - Cpg*T) ./ (delta_hv_0 + Cpv*T); + + % Clear data points beyond 100% relative humidity + Y_h (Y_h > Y_phi) = NaN; + + ax = plot(Y_h*1000,T,'k--'); + label(ax,['h = ', num2str(h/1000), ' kJ/kg'], 'location','center','slope') +end + +hold off +xlabel('Humidity, g vapor / kg dry gas') +ylabel('Temperture, Celsius') + +end \ No newline at end of file diff --git a/mollier_script.m b/mollier_script.m new file mode 100644 index 0000000..a21c906 --- /dev/null +++ b/mollier_script.m @@ -0,0 +1,40 @@ +close all; clearvars; clc + +% Ambient pressure in Pascal +p = 101325; + +% Input temperature array in Celsius +T = -20:80; + +% Water vapor pressure in Pascal +pv_star = (0.61121 * exp((18.678 - T/234.5) .* T./(257.14 + T))) * 1000; + +% Air humidity in kg water per kg dry air +figure +xlim([0,40]) +hold on +for phi = [0.05, 0.2, 0.6, 1.0] % THE LAST MUST BE 1.0 + Y_phi = 18.01/28.96 * phi * pv_star ./ (p - phi * pv_star); + + ax = plot(Y_phi*1000,T,'k'); + label(ax,['\phi = ', num2str(phi)],'location','right','slope') +end + +% Enthalpy of moist air (inverse function) +Cpg = 1000; % air specific heat at constant pressure in J / (kg K) +Cpv = 1860; % water vapor specific heat at constant pressure in J / (kg K) +delta_hv_0 = 2500900; % water vaporization enthalpy at 0°C in J/kg + +for h = [40000, 80000, 120000] + Y_h = (h - Cpg*T) ./ (delta_hv_0 + Cpv*T); + + % Clear data points beyond 100% relative humidity + Y_h (Y_h > Y_phi) = NaN; + + ax = plot(Y_h*1000,T,'k--'); + label(ax,['h = ', num2str(h/1000), ' kJ/kg'], 'location','center','slope') +end + +hold off 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