Plotting Psychrometric Chart using Steam Table in MATLAB
OBJECTIVE OF THE PROJECT :
To construct a simplified psychrometric chart from steam table using MATLAB.
INTRODUCTION :
What is a Psychrometric Chart ?
Psychrometric charts are complex graphs that can be used to assess the physical and thermodynamic properties of gas-vapour mixtures at a constant pressure. They are often used to assess the properties of moist air. This can be useful in the design of heating, ventilation and air-conditioning systems for buildings.
Typically, the properties represented on psychrometric charts are:
- Dry-bulb temperature: A measure of air temperature recorded by a thermometer exposed to the air but shielded from radiation and moisture.
- Wet-bulb temperature: The temperature recorder by a thermometer that has its bulb wrapped in cloth and moistened with distilled water. The rate of evaporation from the wet bulb, and so the temperature it records varies depending on the humidity of the air it is exposed to.
- Relative humidity: The ratio of the actual vapour pressure relative to the vapour pressure of saturated air at the same temperature, expressed as a percentage.
- Specific volume: The volume of a unit weight of dry air.
- Dew Point temperature: The temperature upto which water vapour must be brought at contant pressure for condensation to occur, is called Dew Point Temperature.
- Humidity ratio or Specific Humidity: The dry-basis moisture content of air expressed as the weight of water vapour per unit weight of dry air.
- Enthalpy: The energy content of air.
The state of moist air can be determined from any two of these properties, from which all other properties can then be determined.
Atmospheric pressure varies with altitude and so a number of psychrometric charts are available for different atmospheric pressures. For ground application, we are only concerned about psychrometric chart based on 1 atmospheric pressure.
Hence, the Psychrometric Chart made in this project is based on 1 atmospheric pressure only.
What is a Steam Table ?
Steam tables are defined as the thermodynamic data that contain the properties of water or steam at different Temperature and Pressure. A saturated steam table is an indispensable tool for any engineer working with steam.
Why Steam Table is much important in Psychrometrics?
In psychrometrics we are concerned about properties of moist air. For which, properties of water vapour must be known.
Thus in psychrometrics, Steam Table for low saturation Pressures are of much use as it helps to determine various properties corresponding to the vapour pressure of water vaour.
Why psychrometric Chart ?
Psychrometric Chart is nothing but a redesign of Steam Table with some calculations and is capable of simplifying complex psychrometric problems and calculations.
It is much handy than using a Table. To know the property just 2 variables should be known and that state can be pointed in the chart to know all the other properties.
MOTIVATION FOR THIS PROJECT :
Once, in my 'Refrigeration and Air Conditioning' Class our proffessor told us that Steam Table of water with some calculation is alone sufficient to draw the psychrometric chart.
That motivated me to go for this project.
DATASET USED :
Data is read from 2 datafiles containing water saturation temperature/pressure data, file t_pg over 1 degree C intervals for plotting the saturation and constant relative humidity curves, and file t_pg1 over 5 degree C intervals for plotting the wet-bulb temperature and enthalpy lines. The source of the data : NIST Chemistry WebBook
FORMULAS USED :
Notice in the psychrometric chart that the oblique enthalpy axis is given by = T+5, for T varying between 0°C to 25°C. Substituting this value of in the enthalpy equation (above) leads to the intercept of the enthalpy line with the enthalpy axis as follows:
h = T + 2.5 (T + 5)
or finally: T = (h - 12.5)/3.5
Thus the enthalpy lines can be plotted parallel to, but independant of the wet bulb temperature lines.
MAIN PROGRAM :
%==============================SIMPLIFIED PSYCHROMETRIC CHART============================%
clc
close all
clear all
%======PARSING FILE======%
t_sPv = dlmread('t_pg.txt');
t = t_sPv(:,1);
sPv = t_sPv(:,2);
P_atm = 101.325;
R_air = 0.287;
wg = 622*sPv./(P_atm-sPv);
plot(t,wg,'b-')
hold
grid
%======RELATIVE HUMIDITY LINES======%
for RH = 0.1:0.1:0.4
w = 622*RH*sPv./(P_atm-RH*sPv);
plot(t,w,'color','b')
end
for RH = 0.6:0.2:0.8
w = 622*RH*sPv./(P_atm-RH*sPv);
plot(t,w,'color','b')
end
text(46,7,'10%','color','b')
text(41,9,'20%','color','b')
text(36,11,'30%','color','b')
text(33,12,'40%','color','b')
text(29,14,'60%','color','b')
text(25,15.5,'80%','color','b')
text(22,17,'100%','color','b')
text(40,28,'Relative Humidity','color','b')
text(42,27,'Lines','color','b')
%======PARSING FILE======%
t_sPv1 = dlmread('t_pg1.txt');
t1 = t_sPv1(:,1);
sPv1 = t_sPv1(:,2);
wg1 = 622*sPv1./(P_atm-sPv1);
%======CONSTANT SPECIFIC VOLUME LINES======%
vol = R_air.*(t1+273)./(P_atm-sPv1);
tv0 = P_atm*vol/R_air-273;
for i = 1:7
plot([t1(i) tv0(i)],[wg1(i) 0],'g-')
text(tv0(i),1,num2str(sprintf('%.2f',(vol(i)))),'color',[0 0.5 0],'FontSize',10)
end
text(38,3,'Specific','color',[0 0.5 0])
text(37,2,'Volume Lines','color',[0 0.5 0])
%======CONSTANT WET BULB TEMPERATURE (CONSTANT ENTHALPY) LINES======%
h = 1.005*t1 + wg1*2.5;
t0 = h/1.005;
for i = 1:6,
plot([t1(i),t0(i)],[wg1(i),0],'r-')
text(t1(i)-1,wg1(i)+0.5,num2str(t1(i)),'color','r','FontSize',10)
end
text(13,16,'Wet Bulb','color','r')
text(12,15,'Temp (in deg C)','color','r')
%======ENTHAPLY AXIS======%
for h = 10:10:100
th0 = h/1.005;
th1 = (h-12.5)/3.5;
wh1 = th1 + 5;
plot([th0 th1],[0 wh1], 'k--')
text(th1-1,wh1+0.5,num2str(h),'FontSize',10)
end
text(5,19,'Enthalpy ')
text(4,18,'in KJ/Kg Dry Air)')
plot([0 25],[5,30],'k-')
axis([0,50,0,30])
xticks(0:5:50)
xticklabels(0:5:50)
title('Simplified Psychrometric Chart at 1 atm')
xlabel('Dry Bulb Temperature (deg C)')
ylabel('Specific Humidity (gm vap/kg dry air)')OUTPUT :
REFERENCES :
- https://www.ashrae.org/
- https://nptel.ac.in/content/storage2/courses/112105129/pdf/R&AC%20Lecture%2027.pdf
==================Thankyou===================