Humid air is widely used in various industries, including railway transport in heating, cooling, dehumidifying or humidifying systems. IN Lately A promising direction in the development of air conditioning technology is the introduction of the so-called indirect evaporative cooling method. This is explained by the fact that such devices do not contain artificially synthesized refrigerants; in addition, they are silent and durable, since they do not have moving or quickly wearing elements. To design such devices, it is necessary to have information about the patterns of thermal processes occurring in moist air when its parameters change.
Thermal calculations associated with the use humid air are performed using i-d diagram (see Figure 4), proposed in 1918 by Professor A.K. Ramzin.
This diagram expresses the graphical relationship between the main air temperature parameters, relative humidity, partial pressure, absolute humidity and heat content at a given barometric pressure. To construct it, moisture content d is plotted on the auxiliary 0-d axis on a scale, with an interval corresponding to 1 gram, and vertical lines are drawn through the resulting points. Enthalpy is plotted along the ordinate axis on a scale. i at intervals of 1 kJ/kg dry air. In this case, up from point 0, corresponding to the humid air temperature t = 0 0 C (273 K) and moisture content d = 0, positive ones are laid down, and downwards - negative values 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. Isotherm lines and constant relative humidity lines are applied to the grid thus obtained. 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 Св – respectively temperature (0 С) and heat capacity of dry air (kJ/kg 0 С);
r – latent heat of water vaporization (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 coordinates i–d are straight lines and to construct them 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°С (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 point (i 0) lies at the origin.
. (1.28)
For fully saturated air at a temperature t = 0 ° C (273 K) 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 enthalpy value: (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 humid air at temperature t=0 0 C (273K).
In a similar way, you can construct any other isotherm, for example, for a temperature of plus 10 0 C (283). At this temperature and =100%, according to reference data, we find the partial pressure of fully saturated air equal to P p =9.21 mm. Hg Art. (1.23 kPa), 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 the heat content of moist air (i = 29.35 kJ/g).
For absolutely dry air ( = 0%), at a temperature T = 10 o C (283 K), after substituting the values into expression (1.27), we obtain:
i= 1.005*10= 10.05 kJ/g.
On the i-d diagram we find the coordinates of the corresponding points, and by drawing a straight line through them we obtain an isotherm line for a temperature of plus 10 0 C (283 K). A family of other isotherms is constructed in a similar way, and by combining all isotherms for =100% (on the saturation line) we obtain a line of constant relative humidity =100%.
As a result of the completed constructions, an i-d diagram was obtained, which is shown in Figure 4. Here, the values of moist air temperatures are plotted on the ordinate axis, and the moisture content values are plotted on the abscissa axis. Slanted lines show heat content values (kJ/kg). Curves diverging in a beam from the coordinate center express the relative humidity values φ.
The curve φ=100% is called the saturation curve; above it, water vapor in the air is in a superheated state, and below it is in a state of supersaturation. The inclined line coming from the coordinate center characterizes the partial pressure of water vapor. The partial pressure values are plotted on the right on the y-axis.
Using the i - d diagram, at a given temperature and relative humidity of the air, it is possible to determine its remaining parameters - heat content, moisture content and partial pressure. For example, for a given temperature plus 25°C (273K) and relative humidity and φ=40% on the i - d diagram we find the point A. Moving vertically downwards from it, at the intersection with the inclined line we find the partial pressure P p = 9 mm Hg. Art. (1.23 kPa) and then on the x-axis - moisture content d A = 8 g/kg of dry air. The diagram also shows that the point A lies on an inclined line expressing the heat content i A = 11 kJ/kg dry air.
Processes that occur when air is heated or cooled without changing the moisture content are depicted on the diagram by vertical, straight lines. The diagram shows that when d=const, in the process of heating the air, its relative humidity decreases, and when cooling, it increases.
Using the i – d diagram, you can determine the parameters of the mixed parts of moist air; for this, the so-called angular coefficient of the process beam is built . The construction of a process ray (see Figure 5) starts from a point with known parameters, at in this case this is point 1.
The moist air diagram gives a graphical representation of the relationship between the parameters of moist air and is the main one for determining the parameters of the state of the air and calculating the processes of heat and humidity 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 straight lines of constant moisture content (d = const). Point O is taken as the starting point, at which t = 0 °C, d = 0 g/kg and, therefore, 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 axis of moisture content is drawn at an angle of 90º to the enthalpy axis. The diagram is plotted for constant barometric pressure. Use I-d diagrams built for atmospheric pressure p b = 99.3 kPa (745 mmHg) and atmospheric pressure p b = 101.3 kPa (760 mmHg).
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 diagram field is divided into two parts by the line φ = 100%. 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 convenience of work, a dependence is plotted in the lower part of the diagram; a line of partial pressure of water vapor p p is plotted on the 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 humid air.
Determination of humid air parameters using 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. We determine graphically: dry thermometer temperature t c, moisture content d A, enthalpy I A. Dew point temperature t p is defined as the temperature of the point of intersection of the line d A = const with line φ = 100% (point P). Air parameters in a state of complete saturation with moisture are determined at the intersection of the t A isotherm with the line φ = 100% (point H).
The process of air humidification without supplying or removing heat will take place at a constant enthalpy I A = const ( A-M process). At the intersection of the line I A = const with the line φ = 100% (point M), we find the wet thermometer temperature t m (the line of constant enthalpy practically coincides with the isotherm
t m = const). In unsaturated, humid air, the wet-bulb temperature is lower than the dry-bulb temperature.
We find the partial pressure of water vapor p P by drawing a line d A = const from point A until it intersects with the partial pressure line.
The temperature difference t c – t m = Δt ps is called psychrometric, and the temperature difference t c – t r hygrometric.
The basic properties of moist air can be determined with sufficient accuracy for technical calculations by help i's- diagram developed by L.K. Ramzin (1918). The i-x diagram (Fig. 1, 2) was constructed for a constant pressure p = 745 mm Hg. Art. (about 99 kN/m2), which, according to long-term statistical data, is accepted as the annual average for central regions former USSR.
Enthalpy i is plotted on the ordinate axis on a certain scale, and moisture content x is plotted on the inclined abscissa axis. The angle between the coordinate axes is 135°, but for ease of use, the moisture content x values are projected on an auxiliary axis perpendicular to the ordinate axis.
There are lines on the diagram:
- · constant moisture content (x = const) - vertical straight lines parallel to the ordinate axis;
- · constant enthalpy (i = const) - straight lines, parallel to the abscissa axis, i.e. directed at an angle of 135° to the ordinate axis;
- · constant temperatures, or isotherms (t = const);
- · constant relative humidity (c = const);
- · partial pressures of water vapor (p) in moist air, the values of which are plotted to scale on the right ordinate axis of the diagram.
Rice. 1. Humid air diagram i - x (a)
Lines of constant temperatures, or isotherms, are specified at a given temperature t = const by two arbitrary values x 1 and x 2. The i value corresponding to each x value is then calculated. The resulting points (x 1, i 1) and (x 2, i 2) are plotted on the diagram and a straight line is drawn through them, which is the isotherm t = const.
Lines of constant relative humidity express the relationship between x and p at c = const. Taking at a given q = const several arbitrary temperatures t 1, t 2, t 3 for each of them, the corresponding values of p are found from the tables of water vapor and the corresponding value of x is calculated. Points with known coordinates (t 1, x 1), (t 2, x 2), (t 3, x 3), etc. connected by a curve, which is the line q = const.
Rice. 2.
At temperatures t > 99.4 °C, the value of c does not depend on temperature (since in this case p = 745 mm Hg, for which the diagram was constructed) and is practically a constant value. Therefore, the lines q = const at 99.4 °C have a sharp turn and go almost vertically upward.
The line q = 100% corresponds to the saturation of air with water vapor at a given temperature. Above this line is the working area of the diagram, which corresponds to unsaturated moist air used as a drying agent.
The partial pressure lines drawn at the bottom of the diagram allow you to determine the partial pressure if the position of the point on the diagram corresponding to the state of the air is known.
By i-x diagram Using any two known parameters of moist air, you can find a point characterizing the state of the air and determine all its other parameters.
Using a system of equations including dependencies 4.9, 4.11, 4.17, as well as a functional connection R n = f(t), OK. Ramzin built J-d humid air diagram, which is widely used in the calculations of ventilation and air conditioning systems. This diagram represents a graphical relationship between the main air parameters t, , J, d And R n at a certain barometric air pressure R b.
Construction J-d diagrams are described in detail in the works.
The state of humid air is characterized by a point marked on the field J-d diagram bounded by a line d= 0 and curve = 100%.
The position of the point is specified by any two of the five parameters indicated above, as well as the dew point temperatures t p and wet thermometer t m . The exception is combinations d - R n and d - t r, because each value d only one table value matches R n and t p, and combination J - t m.
The diagram for determining air parameters for a given point 1 is shown in Fig. 1.
Taking advantage J-d diagram in adj. 4 and the diagram in Fig. 1, let's solve specific examples for all 17 possible combinations of given initial air parameters, the specific values of which are indicated in table. 7.
The solution diagrams and the results obtained are shown in Fig. 2.1 ... 2.17. Known parameters air are highlighted in the figures with thick lines.
5.2. Process beam angle on j-d diagram
The ability to quickly graphically determine the parameters of humid air is important, but not the main factor when using J-d diagrams.
As a result of heating, cooling, dehumidifying or humidifying moist air, its heat-humidity state changes. The change processes are depicted in J-d diagram with straight lines that connect points characterizing the initial and final states of air.
Rice. 1. Scheme for determining the parameters of humid air on J-d diagram
Table 7
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Figure number |
Known air parameters |
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t 1 , °C |
kJ/kg d.w. |
R p1, kPa |
t p1, °C |
t m1, °C |
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These lines are called rays of processes changes in air condition. Direction of the process beam to J-d the diagram is determined slope . If the parameters of the initial air state J 1 and d 1 , and the final one – J 2 And d 2, then the slope is expressed by the ratio J/d, i.e.:
.
(5.1)
The magnitude of the slope is measured in kJ/kg moisture.
If in equation (29) the numerator and denominator are multiplied by the mass flow rate of the processed air G, kg/h, then we get:
,
(5.2)
Where Q n is the total amount of heat transferred when the air condition changes, kJ/h;
W- the amount of moisture transferred during the change in air condition, kg/h.
Depending on the ratio J and d the angular coefficient can change its sign and magnitude from 0 to .
In Fig. Figure 3 shows the rays of characteristic changes in the state of moist air and the corresponding values of the angular coefficient.
1. Humid air with initial parameters J 1 and d 1 is heated at constant moisture content to the parameters of point 2, i.e. d 2 = d 1 , J 2 > J 1 . Slope factor the process ray is equal to:
Rice. 3. Angular coefficient on J-d diagram
This process is carried out, for example, in surface air heaters, when the temperature and enthalpy of the air increase, the relative humidity decreases, but the moisture content remains constant.
2. Humid air is simultaneously heated and humidified and acquires the parameters of point 3. The angular coefficient of the process beam 3 > 0. This process occurs when the supply air assimilates heat and moisture in the room.
3. Humid air is humidified at a constant temperature to the parameters of point 4, 4 > 0. In practice, this process is carried out by humidifying the supply or internal air with saturated water vapor.
4. Humid air is humidified and heated with an increase in enthalpy to the parameters of point 5. Since the enthalpy and moisture content of the air increase, then 5 > 0. Typically, this process occurs with direct contact of air with heated water in irrigation chambers and cooling towers.
5. The change in the state of moist air occurs at constant enthalpy J 6 = J 1 = const. The angular coefficient of such a process beam is 6 = 0, because J = 0.
The process of isenthalpic air humidification with circulating water is widely used in air conditioning systems. It is carried out in irrigation chambers or in devices with an irrigated nozzle.
When unsaturated moist air comes into contact with small droplets or a thin film of water without removing or adding heat from the outside, the water humidifies and cools the air through evaporation, acquiring a wet-bulb temperature.
As follows from equation 4.21, in the general case, the angular coefficient of the process beam during isenthalpic humidification is not equal to zero, because
,
Where With w= 4.186 - specific heat capacity of water, kJ/kg°C.
A real isenthalpic process in which = 0 is possible only when t m = 0.
6. Humid air is humidified and cooled to point 7. In this case, the slope is 7< 0, т.к. J 7 – J 1 0, a d 7 – d 1 > 0. This process occurs in irrigation nozzle chambers when air comes into contact with cooled water, which has a temperature above the dew point of the air being processed.
7. Humid air is cooled at constant moisture content to the parameters of point 8. Since d = d 8 – d 1 = 0, a J 8 – J 1 < 0, то 8 = -. Air cooling process d= const occurs in surface air coolers at the heat exchange surface temperature above the air dew point temperature, when there is no moisture condensation.
8. Humid air is cooled and dried to the parameters of point 9. The expression for the slope coefficient in this case has the form:
Cooling with drying occurs in irrigation chambers or surface air coolers when moist air comes into contact with a liquid or solid surface at a temperature below the dew point.
Note that the cooling process with drying with direct contact of air and chilled water is limited by the tangent drawn from point 1 to the saturation curve = 100%.
9. Deep drying and cooling of air to the parameters of point 10 occurs through direct contact of air with a cooled absorbent, for example, a solution of lithium chloride in irrigation chambers or in devices with an irrigation nozzle. Angular coefficient 10 > 0.
10. Humid air is dried, i.e. gives up moisture, at constant enthalpy up to the parameters of point 11. The expression for the angular coefficient has the form
.
This process can be carried out using absorbent solutions or solid adsorbents. Note that the real process will have an angular coefficient 11 = 4.186 t 11, where t 11 - final dry-bulb air temperature.
From Fig. 3. it is clear that all possible changes in the state of moist air are located on the field J-d diagrams in four sectors, the boundaries of which are lines d= const and J= const. In sector I, processes occur with an increase in enthalpy and moisture content, so the values of > 0. In sector II, air is dried with an increase in enthalpy and the value of < 0. В секторе III процессы идут с уменьшением энтальпии и влагосодержания и >0. In sector IV, air humidification processes occur with a decrease in enthalpy, therefore < 0.
With a more strict definition, it should be understood as the ratio of the partial pressures of water vapor pn located 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 humid 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:
From the equation it is clear that with an increase in the partial pressure of steam at constant pressure p(barometric) and temperature T The density of moist air decreases. Since this decrease is insignificant, in practice it is accepted.
Degree of saturation of humid 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, divided by 1 kg dry or (1+d) kg humid air.
The enthalpy of dry air is taken as the zero point ( d= 0) with temperature t= 0°C. Therefore, the enthalpy of moist air can have positive and negative values.
Enthalpy of dry air 
where is the mass heat capacity of dry air.
The enthalpy of water vapor includes the amount of heat required to convert water into steam at t=0 o C and the amount of heat expended to heat the resulting steam to 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 moist air is equal to the sum of enthalpy 1 kg dry air and enthalpy d kg water vapor:
Where 
- 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 is general view
Enthalpy of water =4.19t, enthalpy of ice.
At temperatures above zero degrees ( t>0°C) there will be droplets of moisture in the air, at t< 0°С - кристаллы льда.
Dew point temperature- air temperature at which, in an isobaric cooling process, the partial pressure of water vapor r p becomes equal to the 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 at its constant density becomes due to air cooling with saturated steam(j =100%). For the above examples (see Table 2.1), when at 25 o C absolute humidity j becomes 50%, the dew point will be a temperature of about 14 o C. And when at 20 o C the absolute humidity j becomes 50%, the dew point will be a temperature of about 9 o 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 areas with a continental climate, conditions with a dew point between 15 and 20 °C cause some discomfort, and air with a dew point above 21 °C is perceived as stuffy. Low dew point, less than 10°C, correlates with lower temperature environment, and the body requires less cooling. Low dew point can only go along with high temperature at very low relative humidity.
Diagram d-I of humid air
Calculation and analysis of heat and humidity air treatment processes using the above dependencies is complex. To calculate the processes occurring with air when its state changes, use the thermal diagram of moist air in 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
once-through boiler. http://ru.wikipedia.org/wiki/Ramzin
It has become widespread here and abroad. Diagram d-I humid air graphically connects all parameters that determine the thermal 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.
Most often the diagram d-I built for air pressure equal to 0.1013 MPa(760 mmHg). There are also diagrams for other barometric pressures.
Due to the fact that 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 constructed in an oblique coordinate system (at 135°). At the same time, the diagram becomes convenient for graphical constructions and for calculating air conditioning processes, since the region of unsaturated moist air expands. However, in order to reduce the size of the diagram and ease of use, the values d carried to a conditional axis located at 90° to the axis I .
Diagram d-I is 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 marked on it. t= const, which are not parallel to each other - the higher the temperature of the moist 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 diagram field φ = const. Sometimes a line of partial pressures of water vapor is drawn 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 the point A to the point b, no matter what process, then in the diagram d-I this change can be represented as a straight line segment ab. In this case, the increment in air enthalpy will correspond to the segment bv=I b -I a. Isotherm drawn through a point A, will divide the segment bv into two parts:
line segment bd, representing the change in the proportion of sensible heat (the supply of thermal energy, a change in 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 a change in air moisture content. The dew point is found by lowering a perpendicular from the air condition point (for example, from the point b) on a conditional axis d until it intersects with the saturation line (φ=100%). In 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 the air is characterized by changes in enthalpy I and moisture content d .