After reading this article, I recommend reading the article about enthalpy, latent cooling capacity and determination of the amount of condensate formed in air conditioning and dehumidification systems:
Good day, dear beginner colleagues!
At the very beginning of my professional journey, I came across this diagram. At first glance, it may seem scary, but if you understand the main principles by which it works, then you can fall in love with it: D. In everyday life, it is called i-d diagram.
In this article, I will try to simply (on my fingers) explain the main points, so that later, starting from the received foundation, you will independently delve into this web of air characteristics.
This is what it looks like in textbooks. It gets kind of creepy.
I will remove all that is superfluous that I will not need for my explanation and present the i-d diagram in this form:
(to enlarge the image, click and then click again)
It's still not entirely clear what it is. Let's break it down into 4 elements:
The first element is moisture content (D or d). But before I start talking about air humidity in general, I would like to agree on something with you.
Let's agree "on the shore" at once about one concept. Let's get rid of one firmly entrenched in us (at least in me) stereotype about what steam is. From the very childhood, they pointed me at a boiling pot or teapot and said, poking a finger at the “smoke” coming out of the vessel: “Look! That's steam." But like many people who are friends with physics, we must understand that “Water vapor is a gaseous state water. Doesn't have colors, taste and smell. It's just H2O molecules in the gaseous state, which are not visible. And what we see, pouring out of the kettle, is a mixture of water in a gaseous state (steam) and “water droplets in the boundary state between liquid and gas”, or rather, we see the latter (with reservations, we can also call what we see - mist). As a result, we get that at the moment, around each of us there is dry air (a mixture of oxygen, nitrogen ...) and steam (H2O).
So, the moisture content tells us how much of this vapor is present in the air. On most i-d diagrams, this value is measured in [g / kg], i.e. how many grams of steam (H2O in gaseous state) is in one kilogram of air (1 cubic meter of air in your apartment weighs about 1.2 kilograms). In your apartment for comfortable conditions in 1 kilogram of air there should be 7-8 grams of steam.
On the i-d diagram, the moisture content is depicted by vertical lines, and the gradation information is located at the bottom of the diagram:
(to enlarge the image, click and then click again)
The second important element to understand is air temperature (T or t). I don't think there is any need to explain here. On most i-d diagrams, this value is measured in degrees Celsius [°C]. On the i-d diagram, the temperature is depicted by slanted lines, and the gradation information is located on the left side of the diagram:
(to enlarge the image, click and then click again)The third element of the ID diagram is relative humidity (φ). Relative humidity is exactly the kind of humidity we hear about on TVs and radios when we listen to the weather forecast. It is measured as a percentage [%].
A reasonable question arises: “What is the difference between relative humidity and moisture content?” I will answer this question step by step:
First stage:
Air can hold a certain amount of vapor. Air has a certain “steam load capacity”. For example, in your room, a kilogram of air can “take on board” no more than 15 grams of steam.
Suppose your room is comfortable, and in every kilogram of air in your room there is 8 grams of steam, and each kilogram of air can contain 15 grams of steam. As a result, we get that 53.3% of the maximum possible steam is in the air, i.e. relative humidity - 53.3%.
Second phase:
The air capacity is different at different temperatures. The higher the air temperature, the more steam it can contain, the lower the temperature, the lower the capacity.
Suppose that we have heated the air in your room with a conventional heater from +20 degrees to +30 degrees, but the amount of steam in each kilogram of air remains the same - 8 grams. At +30 degrees, the air can “take on board” up to 27 grams of steam, as a result, in our heated air - 29.6% of the maximum possible steam, i.e. relative humidity - 29.6%.
The same goes for cooling. If we cool the air to +11 degrees, then we get a “carrying capacity” equal to 8.2 grams of steam per kilogram of air and a relative humidity of 97.6%.
Note that there was the same amount of moisture in the air - 8 grams, and the relative humidity jumped from 29.6% to 97.6%. This happened due to temperature fluctuations.
When you hear about the weather on the radio in winter, where they say that it is minus 20 degrees outside and the humidity is 80%, this means that there are about 0.3 grams of vapor in the air. Once in your apartment, this air heats up to +20 and the relative humidity of such air becomes 2%, and this is very dry air (in fact, in the apartment in winter, the humidity is kept at 10-30% due to the release of moisture from the bathrooms, from kitchens and from people, but which is also below the comfort parameters).
Third stage:
What happens if we lower the temperature to such a level that the “carrying capacity” of the air is lower than the amount of vapor in the air? For example, up to +5 degrees, where the air capacity is 5.5 grams / kilogram. That part of the gaseous H2O that does not fit into the “body” (in our case it is 2.5 grams) will begin to turn into a liquid, i.e. in water. In everyday life, this process is especially clearly visible when the windows fog up due to the fact that the temperature of the glasses is lower than the average temperature in the room, so much so that there is little room for moisture in the air and the vapor, turning into a liquid, settles on the glasses.
On the i-d diagram, relative humidity is shown as curved lines, and the gradation information is located on the lines themselves:
(to enlarge the image, click and then click again)
The fourth element of the ID diagram is the enthalpy (I or i). Enthalpy contains the energy component of the heat and moisture state of air. Upon further study (outside of this article, for example in my article on enthalpy ) it is worth paying special attention to it when it comes to dehumidification and humidification of the air. But for now, we will not focus on this element. Enthalpy is measured in [kJ/kg]. On the i-d diagram, the enthalpy is depicted by slanted lines, and the information about the gradation is located on the graph itself (or on the left and in the upper part of the diagram).
Humid air is widely used in various industries, including railway transport in heating, cooling, dehumidification or air humidification systems. Recently, a promising direction in the development of air conditioning technology is the introduction of the so-called indirect evaporative cooling method. This is due to the fact that such devices do not contain artificially synthesized refrigerants, in addition, they are silent and durable, since they do not have moving and quickly wearing out elements. For the design of such devices, it is necessary to have information about the patterns of heat engineering processes occurring in moist air when its parameters change.
Thermotechnical calculations related to the use of humid air are performed using i-d diagram (see Figure 4), proposed in 1918 by Professor A.K. Ramzin.
This diagram expresses the graphical dependence of the main parameters of air-temperature, relative humidity, partial pressure, absolute humidity and heat content at a given barometric pressure. To build it on the auxiliary axis 0-d on a scale, with an interval corresponding to 1 gram, the moisture content d is laid down and vertical lines are drawn through the points obtained. Enthalpy is plotted along the y-axis on a scale i with an interval of 1 kJ/kg of dry air. At the same time, upwards from point 0, corresponding to the temperature of moist air t=0 0 С (273K) and moisture content d=0, positive values of enthalpy are set aside, and downwards - negative values of enthalpy.
Through the obtained points on the ordinate axis, lines of constant enthalpies are drawn at an angle of 135 0 to the abscissa axis. On the grid thus obtained, isotherm lines and lines of constant relative humidity are applied. To construct isotherms, we use the equation for the heat content of moist air:
It can be written in the following form:
, (1.27)
where t and C st are the temperature (0 C) and the heat capacity of dry air (kJ / kg 0 C), respectively;
r is the latent heat of vaporization of water (in calculations it is assumed
r = 2.5 kJ/g).
If we assume that t=const, then equation (1.27) will be a straight line, which means that the isotherms in the coordinates i–d are straight lines and for their construction it is necessary to determine only two points characterizing the two extreme positions of moist air.
Figure 4. i - d diagram of humid air
To construct an isotherm corresponding to the temperature value t=0°C (273K), first, using expression (1.27), we determine the position of the heat content coordinate (i 0) for absolutely dry air (d=0). After substituting the corresponding values of the parameters t=0 0 C (273K) and d=0 g/kg, expression (1.27) shows that the point (i 0) lies at the origin.
. (1.28)
For fully saturated air at a temperature of t=0°C (273K) and =100% from the reference literature, for example, we find the corresponding value of moisture content d 2 =3.77 g/kg dry. air and from expression (1.27) we find the corresponding value of enthalpy: (i 2 = 2.5 kJ / g). In the i-d coordinate system, we plot points 0 and 1 and draw a straight line through them, which will be the isotherm of moist air at a temperature of t=0 0 С (273K).
Any other isotherm can be constructed in a similar way, for example, for a temperature of plus 10 0 C (283). At this temperature and \u003d 100%, according to the reference data, we find the partial pressure of fully saturated air equal to P p \u003d 9.21 mm. rt. Art. (1.23kPa), then from expression (1.28) we find the value of moisture content (d=7.63 g/kg), and from expression (1.27) we determine the value of heat content of moist air (i=29.35 kJ/g).
For absolutely dry air (=0%), at a temperature of T=10 o C (283K), after substituting the values into expression (1.27), we get:
i \u003d 1.005 * 10 \u003d 10.05 kJ / g.
On the i-d diagram, we find the coordinates of the corresponding points, and drawing a straight line through them, we get an isotherm line for a temperature of plus 10 0 C (283K). A family of other isotherms is built in a similar way, and by connecting all isotherms for =100% (on the saturation line) we get a line of constant relative humidity =100%.
As a result of the constructions, an i-d diagram was obtained, which is shown in Figure 4. Here, the values of humid air temperatures are plotted on the y-axis, and the values of moisture content are plotted on the abscissa. Slanted lines show heat content values (kJ/kg). The curves diverging in a beam from the center of coordinates express the values of relative humidity φ.
The curve φ=100% is called the saturation curve; above it, the water vapor in the air is in a superheated state, and below it is in a state of supersaturation. The inclined line from the center of coordinates characterizes the partial pressure of water vapor. The partial pressure values are plotted on the right side of the y-axis.
Using the i - d diagram, it is possible, at a given temperature and relative humidity, to determine its remaining parameters - heat content, moisture content and partial pressure. For example, for a given temperature plus 25°С (273K) and relative humidity and φ=40% on the diagram i - d we find the point BUT. Moving from it vertically down, at the intersection with the inclined line, we find the partial pressure P p = 9 mm Hg. Art. (1.23 kPa) and further on the abscissa - moisture content d A = 8 g / kg of dry air. The diagram also shows that the point BUT lies on an inclined line expressing the heat content i A = 11 kJ/kg dry air.
The processes that occur during heating or cooling of air without changing the moisture content are depicted in the diagram by vertical, straight lines. The diagram shows that at d=const, in the process of heating the air, its relative humidity decreases, and when cooled, it increases.
Using the diagram i - d, it is possible to determine the parameters of the mixed parts of moist air; for this, the so-called angular coefficient of the beam of the process is built . The construction of the process ray (see Figure 5) starts from a point with known parameters, in this case point 1.
Moist air is a mixture of dry air and water vapour. The properties of moist air are characterized by the following main parameters: dry bulb temperature t, barometric pressure P b, partial pressure of water vapor P p, relative humidity φ, moisture content d, specific enthalpy i, dew point temperature t p, wet bulb temperature t m, density ρ.
The i-d diagram is a graphical relationship between the main air parameters t, φ, d, i at a certain barometric air pressure P b and is used to visualize the results of calculating moist air processing processes.
The i-d diagram was first compiled in 1918 by the Soviet heating engineer L.K. Ramzin.
The diagram is built in an oblique coordinate system, which allows expanding the area of unsaturated moist air and makes the diagram convenient for graphic constructions. The values of specific enthalpy i are plotted along the ordinate axis of the diagram, and the values of moisture content d are plotted along the abscissa axis, directed at an angle of 135° to the i axis. The diagram field is divided by lines of constant values of specific enthalpy i=const and moisture content d=const. The diagram also shows lines of constant temperature values t = const, which are not parallel to each other, and the higher the temperature of humid air, the more the isotherms deviate upward. Lines of constant values of relative humidity φ=const are also plotted on the diagram field.
relative humidity is the ratio of the partial pressure of water vapor contained in moist air of a given state to the partial pressure of saturated water vapor at the same temperature.
Moisture content- this is the mass of water vapor in moist air per 1 kg of the mass of its dry part.
Specific enthalpy- this is the amount of heat contained in moist air at a given temperature and pressure, related to 1 kg of dry air.
The i-d diagram of the φ=100% curve is divided into two areas. The entire area of the diagram above this curve characterizes the parameters of unsaturated moist air, and below - the fog area.
Fog is a two-phase system consisting of saturated moist air and suspended moisture in the form of tiny drops of water or ice particles.
To calculate the parameters of humid air and build an i-d diagram, four basic equations are used:
1) Pressure of saturated water vapor above a flat surface of water (t > 0) or ice (t ≤ 0), kPa:
where α in, β in - constants for water, α in \u003d 17.504, β in \u003d 241.2 ° С
α l, β l - constants for ice, α l \u003d 22.489, β l \u003d 272.88 ° С
2) Relative humidity φ, %:
where P b - barometric pressure, kPa
4) Specific enthalpy of moist air i, kJ/kg w.m.:
Dew point temperature is the temperature to which unsaturated air must be cooled to become saturated while maintaining a constant moisture content.
To find the dew point temperature on the i-d diagram through a point characterizing the state of the air, you need to draw a line d=const until it intersects with the curve φ=100%. The dew point temperature is the limiting temperature to which moist air can be cooled at a constant moisture content without condensation.
Wet bulb temperature- this is the temperature that unsaturated moist air takes with initial parameters i 1 and d 1 as a result of adiabatic heat and mass transfer with water in a liquid or solid state, having a constant temperature t in \u003d t m after it reaches a saturated state that satisfies the equality:
where c in - specific heat capacity of water, kJ / (kg ° C)
The difference i n - i 1 is usually small, therefore the process of adiabatic saturation is often called isoenthalpic, although in reality i n = i 1 only at t m = 0.
To find the temperature of the wet thermometer on the i-d diagram through a point characterizing the state of the air, you need to draw a line of constant enthalpy i=const until it intersects with the curve φ=100%.
The density of moist air is determined by the formula, kg / m 3:
where T is the temperature in degrees Kelvin
The amount of heat required to heat the air can be calculated by the formula, kW:
The amount of heat removed from the air during cooling, kW:
where i 1 , i 2 - specific enthalpy at the initial and final points, respectively, kJ / kg s.v.
G s - dry air consumption, kg / s
where d 1 , d 2 - moisture content at the start and end points, respectively, g/kg d.m.
When mixing two air flows, the moisture content and specific enthalpy of the mixture are determined by the formulas:
In the diagram, the mixture point lies on the straight line 1-2 and divides it into segments inversely proportional to the mixed amounts of air:
|
It is possible that the mixture point 3* will be below the line φ=100%. In this case, the mixing process is accompanied by the condensation of part of the water vapor contained in the mixture and the mixture point 3 will lie at the intersection of the lines i 3* =const and φ=100%.
On the presented site on the "Calculations" page, you can calculate up to 8 states of humid air with the construction of process rays on the i-d diagram.
To determine the initial state, you need to specify two of the four parameters (t, φ, d, i) and the flow rate of dry air L c *. The flow rate is set assuming an air density of 1.2 kg/m 3 . From here, the mass flow rate of dry air is determined, which is used in further calculations. The output table displays the actual values of the volumetric air flow corresponding to the actual air density.
The new state can be calculated by defining the process and setting the end parameters.
The diagram shows the following processes: heating, cooling, adiabatic cooling, steam humidification, mixing and the general process, determined by any two parameters.
| Process | Designation | Description |
| Heat | O | The desired final temperature or the desired heat output is entered. |
| Cooling | C | The target end temperature or the target cooling capacity is entered. This calculation is based on the assumption that the surface temperature of the cooler remains unchanged, and the initial air parameters tend to the point with the surface temperature of the cooler at φ=100%. As if there is a mixture of air of the initial state with fully saturated air at the surface of the cooler. |
| Adiabatic cooling | A | The target final relative humidity, either moisture content or temperature, is entered. |
| Steam humidification | P | The specified final relative humidity, or moisture content, is entered. |
| General Process | X | The values of two of the four parameters (t, φ, d, i) are entered, which are final for the given process. |
| Mixing | S | This process is defined without setting parameters. The two previous air flow rates are used. If the maximum permissible moisture content is reached during mixing, then adiabatic condensation of water vapor occurs. As a result, the amount of condensed moisture is calculated. |
LITERATURE:
1. Burtsev S.I., Tsvetkov Yu.N. Wet air. Composition and properties: Proc. allowance. - St. Petersburg: SPbGAHPT, 1998. - 146 p.
2. Handbook ABOK 1-2004. Wet air. - M.: AVOK-PRESS, 2004. - 46 p.
3. ASHRAE Handbook. fundamentals. - Atlanta, 2001.
With a more rigorous definition, it should be understood as the ratio of the partial pressures of water vapor pn in unsaturated moist air to their partial pressure in saturated air at the same temperature
For the temperature range typical for air conditioning
Density of moist air
ρ
equal to the sum of the densities of dry air and water vapor
where is the density of dry air at a given temperature and pressure, kg / m 3.
To calculate the density of moist air, you can use another formula:
It can be seen from the equation that with an increase in the partial pressure of vapor at constant pressure p(barometric) and temperature T the density of moist air decreases. Since this decrease is insignificant, in practice they accept.
The degree of saturation of moist airψ - the ratio of its moisture content d to the moisture content of saturated air at the same temperature: .
For saturated air.
Enthalpy of moist airI(kJ / kg) - the amount of heat contained in the air, referred to 1 kg dry or (1+d) kg humid air.
The zero point is taken as the enthalpy of dry air ( d= 0) with temperature t= 0°С. Therefore, the enthalpy of moist air can have positive and negative values.
Dry air enthalpy 
where is the mass heat capacity of dry air.
The enthalpy of water vapor includes the amount of heat required to turn water into steam at t\u003d 0 o C and the amount of heat spent on heating the resulting steam to a temperature t o C. Enthalpy d kg of water vapor contained in 1 kg dry air: ,
2500 - latent heat of vaporization (evaporation) of water at t=0 o C;
- mass heat capacity of water vapor.
The enthalpy of humid air is equal to the sum of enthalpy 1 kg dry air and enthalpy d kg of water vapor:
where 
is the heat capacity of moist air per 1 kg of dry air.
When the air is in a foggy state, there may be suspended droplets of moisture in it. d water and even ice crystals d l. The enthalpy of such air in general terms
Enthalpy of water =4.19t, enthalpy of ice .
At temperatures above zero degrees t>0°C) there will be moisture in the air, when t< 0°С - кристаллы льда.
Dew point temperature- air temperature at which in the isobaric cooling process the partial pressure of water vapor r p becomes equal to saturation pressure. At this temperature, moisture begins to fall out of the air.
Those. The dew point is the temperature at which water vapor in the air with its constant density becomes due to air cooling by saturated steam(j =100%). For the above examples (see Table 2.1), when at 25 ° C the absolute humidity j becomes 50%, the dew point will be a temperature of about 14 ° C. And when at 20 ° C absolute humidity j becomes 50%, the dew point will be around 9°C.
A person feels uncomfortable at high dew point values (see Table 2.2).
Table 2.2 - Human sensations at high dew point values
In continental climates, conditions with a dew point between 15 and 20 °C are somewhat uncomfortable, and air with a dew point above 21 °C is perceived as stuffy. A lower dew point of less than 10°C correlates with a lower ambient temperature and the body requires less cooling. The low dew point can only go along with the high temperature at very low relative humidity.
Diagram d-I humid air
The calculation and analysis of the processes of heat and moisture treatment of air according to the above dependencies is complex. To calculate the processes that occur with air when its state changes, use the thermal diagram of moist air in the coordinates d-I(moisture content - enthalpy), which was proposed by our compatriot Professor L.K. Ramzin in 1918.
L. K. Ramzin (1887-1948) - Soviet heating engineer, inventor
straight-through boiler. http://ru.wikipedia.org/wiki/Ramzin
It has become widespread in our country and abroad. Diagram d-I humid air graphically connects all the parameters that determine the heat and moisture state of air: enthalpy, moisture content, temperature, relative humidity, partial pressure of water vapor.
The construction of the diagram is based on dependency.
The most common chart d-I is built for an air pressure of 0.1013 MPa(760 mm Hg). There are also diagrams for other barometric pressures.
Since barometric pressure at sea level varies from 0.096 to 0.106 MPa(720 - 800 mm Hg), the calculated data on the diagram should be considered as average.
The diagram is built in an oblique coordinate system (under 135 °). In this case, the diagram becomes convenient for graphical constructions and for calculations of air conditioning processes, since the area of unsaturated moist air expands. However, in order to reduce the size of the chart and make it easier to use, the values d demolished on a conditional axis located at 90 ° to the axis I .
Diagram d-I shown in Figure 1. The diagram field is divided by lines of constant enthalpy values I= const and moisture content d= const. Lines of constant temperature values are also plotted on it. t= const, which are not parallel to each other - the higher the temperature of humid air, the more its isotherms deviate upward. In addition to lines of constant values I, d, t, lines of constant values of relative air humidity are plotted on the chart field φ = const. Sometimes a line of partial pressures of water vapor is applied r p and lines of other parameters.
Figure 1 - Thermal diagram d-I humid air
The following property of the diagram is essential. If the air has changed its state from a point a to the point b, no matter what process, then on the diagram d-I this change can be represented as a line segment ab. In this case, the increment of the enthalpy of air will correspond to the segment bv \u003d I b -I a. Isotherm through a point a, divide the segment bv into two parts:
line segment bd, representing the change in the share of sensible heat (the stock of thermal energy, the change of which leads to a change in body temperature): 
.
line segment dv, which determines on a scale the change in the heat of vaporization (a change in this heat does not cause a change in body temperature): 
.
Line segment ag corresponds to the change in the moisture content of the air. The dew point is found by lowering the perpendicular from the air state point (for example, from the point b) on the conditional axis d to the intersection with the saturation line (φ=100%). On fig. 2.6 K-dew point for air, the initial state of which was determined by the point b.
The direction of the process occurring in air is characterized by changes in enthalpy I and moisture content d .
The diagram of humid air gives a graphical representation of the relationship between the parameters of humid air and is the basis for determining the parameters of the state of the air and calculating the processes of heat and moisture treatment.
In the I-d diagram (Fig. 2), the moisture content d g / kg of dry air is plotted along the abscissa axis, and the enthalpy I of moist air is plotted along the ordinate axis. The diagram shows vertical lines of constant moisture content (d = const). The point O is taken as the reference point, at which t = 0 °C, d = 0 g/kg, and, consequently, I = 0 kJ/kg. When constructing the diagram, an oblique coordinate system was used to increase the area of unsaturated air. The angle between the direction of the axes is 135° or 150°. For ease of use, a conditional moisture content axis is drawn at an angle of 90º to the enthalpy axis. The diagram is built for constant barometric pressure. Use I-d diagrams built for atmospheric pressure p b = 99.3 kPa (745 mm Hg) and atmospheric pressure p b = 101.3 kPa (760 mm Hg).
The diagram shows isotherms (t c = const) and relative humidity curves (φ = const). Equation (16) shows that the isotherms in the I-d diagram are straight lines. The entire field of the diagram is divided by the line φ = 100% into two parts. Above this line is an area of unsaturated air. On the line φ = 100% are the parameters of saturated air. Below this line are the parameters of the state of saturated air containing suspended droplet moisture (fog).
For the convenience of work, a dependence is plotted in the lower part of the diagram, a line is plotted for the partial pressure of water vapor p p on moisture content d. The pressure scale is located on the right side of the diagram. Each point on the I-d diagram corresponds to a certain state of moist air.
Determination of moist air parameters according to the I-d diagram. The method for determining the parameters is shown in fig. 2. The position of point A is determined by two parameters, for example, temperature t A and relative humidity φ A. Graphically we determine: dry thermometer temperature t c, moisture content d A, enthalpy I A. The dew point temperature t p is defined as the temperature of the point of intersection of the line d A = const with the line φ = 100% (point Р). Air parameters in a state of complete saturation with moisture are determined at the intersection of the isotherm t A with the line φ \u003d 100% (point H).
The process of air humidification without heat supply and removal will take place at a constant enthalpy I A = const (process A-M). At the intersection of the line I A \u003d const with the line φ \u003d 100% (point M), we find the temperature of the wet thermometer t m (the line of constant enthalpy practically coincides with the isotherm
t m = const). In unsaturated moist air, the temperature of the wet bulb is less than the temperature of the dry bulb.
We find the partial pressure of water vapor p P by drawing a line d A \u003d const from point A to the intersection with the line of partial pressure.
The temperature difference t s - t m = Δt ps is called psychrometric, and the temperature difference t s - t p hygrometric.
