Define parameters humid air, as well as to solve a number of practical issues related to the drying of various materials, very conveniently in a graphical way with i-d diagrams, first proposed by the Soviet scientist L.K. Ramzin in 1918.

Built for a barometric pressure of 98 kPa. In practice, the diagram can be used in all cases of calculating dryers, since with normal fluctuations in atmospheric pressure, the values i And d change little.

Chart in coordinates i-d is a graphical interpretation of the enthalpy equation for moist air. It reflects the relationship of the main parameters of humid air. Each point on the diagram highlights some state with well-defined parameters. To find any of the characteristics of moist air, it is enough to know only two parameters of its state.

The I-d diagram of humid air is built in an oblique coordinate system. On the y-axis up and down from the zero point (i \u003d 0, d \u003d 0), the enthalpy values ​​\u200b\u200bare plotted and lines i \u003d const are drawn parallel to the abscissa axis, that is, at an angle of 135 0 to the vertical. In this case, the 0 o C isotherm in the unsaturated region is located almost horizontally. As for the scale for reading the moisture content d, for convenience it is taken down to a horizontal straight line passing through the origin.

The curve of the partial pressure of water vapor is also plotted on the i-d diagram. For this purpose, the following equation is used:

R p \u003d B * d / (0.622 + d),

For variable values ​​of d, we obtain that, for example, for d=0 P p =0, for d=d 1 P p = P p1 , for d=d 2 P p = P p2, etc. Given a certain scale for partial pressures, in the lower part of the diagram in a rectangular system of coordinate axes, a curve P p =f(d) is plotted at the indicated points. After that, curved lines of constant relative humidity (φ = const) are plotted on the i-d chart. The lower curve φ = 100% characterizes the state of air saturated with water vapor ( saturation curve).

Also, straight lines of isotherms (t = const) are built on the i-d diagram of humid air, characterizing the processes of moisture evaporation, taking into account the additional amount of heat introduced by water having a temperature of 0 ° C.

In the process of evaporation of moisture, the enthalpy of air remains constant, since the heat taken from the air for drying materials returns back to it along with the evaporated moisture, that is, in the equation:

i = i in + d*i p

A decrease in the first term will be compensated by an increase in the second term. On the i-d diagram, this process goes along the line (i = const) and has the conditional name of the process adiabatic evaporation. The limit of air cooling is the adiabatic temperature of the wet bulb, which is found on the diagram as the temperature of the point at the intersection of the lines (i = const) with the saturation curve (φ = 100%).

Or in other words, if from point A (with coordinates i = 72 kJ / kg, d = 12.5 g / kg dry air, t = 40 ° C, V = 0.905 m 3 / kg dry air φ = 27%), emitting a certain state of moist air, draw down a vertical beam d = const, then it will be a process of cooling the air without changing its moisture content; the value of the relative humidity φ in this case gradually increases. When this beam continues until it intersects with the curve φ = 100% (point "B" with coordinates i = 49 kJ/kg, d = 12.5 g/kg dry air, t = 17.5 °C, V = 0 ,84 m 3 / kg dry air j \u003d 100%), we get the lowest temperature t p (it is called dew point temperature), at which air with a given moisture content d is still able to retain vapors in an uncondensed form; a further decrease in temperature leads to the loss of moisture either in suspension (fog), or in the form of dew on the surfaces of the fences (car walls, products), or frost and snow (evaporator pipes of the refrigeration machine).

If the air in state A is humidified without heat supply or removal (for example, from an open water surface), then the process characterized by the AC line will occur without changing the enthalpy (i = const). Temperature t m at the intersection of this line with the saturation curve (point "C" with coordinates i \u003d 72 kJ / kg, d \u003d 19 g / kg dry air, t \u003d 24 ° C, V \u003d 0.87 m 3 / kg dry air φ = 100%) and is wet bulb temperature.

Using i-d, it is convenient to analyze the processes that occur when moist air flows are mixed.

Also i-d diagram humid air are widely used to calculate the parameters of air conditioning, which is understood as a set of means and methods of influencing the temperature and humidity of the air.

For practical purposes, it is most important to calculate the cooling time of the cargo using the equipment available on board the vessel. Since the capabilities of a ship installation for liquefying gases largely determine the time the vessel stays in the port, knowledge of these capabilities will allow planning the layover time in advance, avoiding unnecessary downtime, and hence claims against the ship.

Mollier diagram. which is given below (Fig. 62), is calculated only for propane, but the method of its use for all gases is the same (Fig. 63).

The Mollier chart uses a logarithmic absolute pressure scale (R log) - on the vertical axis, on the horizontal axis h - natural scale of specific enthalpy (see Fig. 62, 63). Pressure is in MPa, 0.1 MPa = 1 bar, so we will use bars in the future. Specific enthalpy is measured in kJ/kg. In the future, when solving practical problems, we will constantly use the Mollier diagram (but only its schematic representation in order to understand the physics of thermal processes occurring with the load).

In the diagram, one can easily notice a kind of "net" formed by the curves. The boundaries of this "net" outline the boundary curves for the change in the aggregate states of liquefied gas, which reflect the transition of the LIQUID into saturated steam. Everything to the left of the "net" refers to supercooled liquid, and everything to the right of the "net" refers to superheated steam (see Fig. 63).

The space between these curves represents different states of a mixture of saturated propane vapor and liquid, reflecting the phase transition process. On a number of examples, we will consider the practical use * of the Mollier diagram.

Example 1: Draw a line corresponding to a pressure of 2 bar (0.2 MPa) through the section of the diagram reflecting the phase change (Fig. 64).

To do this, we determine the enthalpy for 1 kg of boiling propane at an absolute pressure of 2 bar.

As noted above, boiling liquid propane is characterized by the left curve of the diagram. In our case, this will be the point A, Swiping from a point A vertical line to scale A, we determine the value of enthalpy, which will be 460 kJ / kg. This means that each kilogram of propane in this state (at the boiling point at a pressure of 2 bar) has an energy of 460 kJ. Therefore, 10 kg of propane will have an enthalpy of 4600 kJ.

Next, we determine the enthalpy value for dry saturated propane steam at the same pressure (2 bar). To do this, draw a vertical line from the point IN to the intersection with the enthalpy scale. As a result, we find that the maximum enthalpy value for 1 kg of propane in the saturated vapor phase will be 870 kJ. Inside the chart

* For calculations, data from the thermodynamic tables of propane are used (see Appendixes).

Rice. 64. For example 1 Fig. 65. Example 2

At
effective enthalpy, kJ/kg (kcal/kg)

Rice. 63. Basic curves of the Mollier diagram

(Fig. 65) the lines directed downward from the point of the critical state of the gas represent the number of parts of the gas and liquid in the transition phase. In other words, 0.1 means that the mixture contains 1 part gas vapor and 9 parts liquid. At the point of intersection of the saturated vapor pressure and these curves, we determine the composition of the mixture (its dryness or humidity). The transition temperature is constant throughout the condensation or vaporization process. If propane is in a closed system (cargo tank), both the liquid and gaseous phases of the cargo are present. The temperature of a liquid can be determined from the vapor pressure, and the vapor pressure from the temperature of the liquid. Pressure and temperature are related if liquid and vapor are in equilibrium in a closed system. Note that the temperature curves located on the left side of the diagram descend almost vertically, cross the vaporization phase in the horizontal direction, and on the right side of the diagram again descend almost vertically.

Example 2: Assume that there is 1 kg of propane in the phase change stage (part of the propane is liquid and part is vapor). The saturated vapor pressure is 7.5 bar and the enthalpy of the mixture (vapor-liquid) is 635 kJ/kg.

It is necessary to determine which part of the propane is in the liquid phase and which is in the gaseous phase. Let us put on the diagram first of all the known quantities: vapor pressure (7.5 bar) and enthalpy (635 kJ/kg). Next, we determine the point of intersection of pressure and enthalpy - it lies on the curve, which is labeled 0.2. And this, in turn, means that we have propane in the boiling stage, and 2 (20%) parts of propane are in a gaseous state, and 8 (80%) are in a liquid state.

It is also possible to determine the gauge pressure of a liquid in a tank whose temperature is 60° F, or 15.5° C (we will use the propane thermodynamic table from the Appendix to convert the temperature).

It must be remembered that this pressure is less than the saturated vapor pressure (absolute pressure) by the value of atmospheric pressure, equal to 1.013 mbar. In the future, to simplify the calculations, we will use the value of atmospheric pressure equal to 1 bar. In our case, the saturated vapor pressure, or absolute pressure, is 7.5 bar, so the gauge pressure in the tank will be 6.5 bar.

Rice. 66. Example 3

It was already mentioned earlier that liquid and vapors in an equilibrium state are in a closed system at the same temperature. This is true, but in practice it can be seen that the vapors located in the upper part of the tank (in the dome) have a temperature much higher than the temperature of the liquid. This is due to the heating of the tank. However, such heating does not affect the pressure in the tank, which corresponds to the temperature of the liquid (more precisely, the temperature at the surface of the liquid). Vapors directly above the surface of the liquid have the same temperature as the liquid itself on the surface, where the phase change of the substance occurs.

As can be seen from fig. 62-65, in the Mollier diagram, the density curves are directed from the lower left corner of the "net" diagram to the upper right corner. The density value on the chart can be given in Ib/ft 3 . For conversion to SI, a conversion factor of 16.02 is used (1.0 Ib / ft 3 \u003d 16.02 kg / m 3).

Example 3: In this example we will use density curves. It is required to determine the density of superheated propane vapor at an absolute pressure of 0.95 bar and a temperature of 49 ° C (120 ° F).
We also determine the specific enthalpy of these vapors.

The solution of the example can be seen from Figure 66.

In our examples, the thermodynamic characteristics of one gas, propane, are used.

In such calculations for any gas, only the absolute values ​​of the thermodynamic parameters will change, but the principle remains the same for all gases. In what follows, for simplification, greater accuracy of calculations, and reduction of time, we will use tables of thermodynamic properties of gases.

Almost all the information included in the Mollier diagram is presented in tabular form.

WITH
using tables, you can find the values ​​of the parameters of the load, but it is difficult. Rice. 67. For example 4 imagine how the process is going. . cooling, if you do not use at least a schematic display of the diagram p- h.

Example 4: There is propane in a cargo tank at a temperature of -20 "C. It is necessary to determine as accurately as possible the pressure of the gas in the tank at a given temperature. Next, it is necessary to determine the density and enthalpy of vapor and liquid, as well as the difference" enthalpy between liquid and vapor. Vapors above the surface of a liquid are in saturation at the same temperature as the liquid itself. Atmospheric pressure is 980 mlbar. It is necessary to build a simplified Mollier diagram and display all the parameters on it.

Using the table (see Appendix 1), we determine the pressure of saturated vapors of propane. Absolute pressure propane vapor at -20 ° C is 2.44526 bar. The pressure in the tank will be:

tank pressure (gauge or gauge)

1.46526 bar

atmospheric pressure= 0.980 bar =

Absolute _ pressure

2.44526 bar

In the column corresponding to the density of the liquid, we find that the density of liquid propane at -20 ° C will be 554.48 kg / m 3. Next, we find in the corresponding column the density of saturated vapors, which is equal to 5.60 kg / m 3. The enthalpy of liquid will be 476.2 kJ/kg, and that of vapor - 876.8 kJ/kg. Accordingly, the enthalpy difference will be (876.8 - 476.2) = 400.6 kJ / kg.

Somewhat later, we will consider the use of the Mollier diagram in practical calculations to determine the operation of reliquefaction plants.

The I-d diagram of humid air was developed by the Russian scientist, Professor L.K. Ramzin in 1918. In the West, the analogue of the I-d-diagram is the Mollier diagram or the psychrometric diagram. The I-d-diagram is used in the calculations of air conditioning, ventilation and heating systems and allows you to quickly determine all the parameters of air exchange in the room.

I-d-diagram of 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. Using a diagram allows you to visually display the ventilation process, avoiding complex calculations using formulas.

Basic properties of moist air

The air around us is a mixture of dry air and water vapour. This mixture is called moist air. Humid air is evaluated according to the following main parameters:

• Air temperature according to dry thermometer tc, °C - characterizes the degree of its heating;
• Wet-bulb air temperature tm, °C - the temperature to which the air must be cooled to become saturated while maintaining the initial enthalpy of the air;
• Air dew point temperature tp, °C - the temperature to which unsaturated air must be cooled so that it becomes saturated while maintaining a constant moisture content;
• Moisture content of air d, g / kg - this is the amount of water vapor in g (or kg) per 1 kg of the dry part of moist air;
• Relative humidity j, % - characterizes the degree of air saturation with water vapor. This is the ratio of the mass of water vapor contained in the air to their maximum possible mass in the air under the same conditions, that is, temperature and pressure, and expressed as a percentage;
• Saturated state of humid air - a state in which the air is saturated with water vapor to the limit, for it j \u003d 100%;
• Absolute air humidity e, kg / m 3 - this is the amount of water vapor in g contained in 1 m 3 of moist air. Numerically absolute humidity air is equal to the density of moist air;
• Specific enthalpy of humid air I, kJ/kg - the amount of heat required to heat from 0 ° C to a given temperature such an amount of humid air, the dry part of which has a mass of 1 kg. The enthalpy of humid air is the sum of the enthalpy of its dry part and the enthalpy of water vapor;
• Specific heat of humid air c, kJ / (kg.K) - the heat that must be spent on one kilogram of humid air in order to increase its temperature by one degree Kelvin;
• Partial pressure of water vapor Pp, Pa - pressure under which water vapor is in humid air;
• The total barometric pressure Pb, Pa is equal to the sum of the partial pressures of water vapor and dry air (according to Dalton's law).

Description of the I-d diagram

The ordinate axis of the diagram shows the values ​​of enthalpy I, kJ/kg of the dry part of the air; the abscissa axis, directed at an angle of 135° to the I axis, shows the values ​​of the moisture content d, g/kg of the dry part of the air. The diagram field is divided by lines of constant values ​​of enthalpy I = const and moisture content d = const. It also has lines of constant temperature values ​​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 ​​of I, d, t, lines of constant values ​​of relative air humidity φ = const are plotted on the diagram field. In the lower part of the I-d-diagram there is a curve with an independent y-axis. It relates the moisture content d, g/kg, to the water vapor pressure Rp, kPa. The y-axis of this graph is the scale of the partial pressure of water vapor Pp. The entire field of the diagram is divided by the line j = 100% into two parts. Above this line is an area of ​​unsaturated moist air. Line j = 100% corresponds to the state of air saturated with water vapor. Below is an area of ​​supersaturated air (fog area). Each point on the I-d-diagram corresponds to a certain heat and moisture state. The line on the I-d-diagram corresponds to the process of heat and moisture treatment of air. General form I-d-diagrams of humid air are presented below in the attached PDF file suitable for printing in A3 and A4 formats.

Construction of air treatment processes in air conditioning and ventilation systems on the I-d-diagram.

Heating, cooling and air mixing processes

On the I-d-diagram of moist air, the processes of heating and cooling of air are depicted by rays along the line d-const (Fig. 2).

Rice. 2. The processes of dry heating and cooling of air on the I-d-diagram:

• V_1, V_2, - dry heating;
• В_1, В_3 – dry cooling;
• В_1, В_4, В_5 – cooling with dehumidification.

The processes of dry heating and dry air cooling are carried out in practice using heat exchangers (air heaters, air heaters, air coolers).

If the moist air in the heat exchanger is cooled below the dew point, then the cooling process is accompanied by condensation from the air on the surface of the heat exchanger, and air cooling is accompanied by its drying.

Considering what is the main object of the ventilation process, in the field of ventilation it is often necessary to determine certain air parameters. To avoid numerous calculations, they are usually determined by a special diagram, which is called the Id of the diagram. It allows you to quickly determine all air parameters from two known ones. Using a diagram allows you to avoid formula calculations and visually display the ventilation process. An example chart Id is shown on the next page. The analogue of the Id chart in the west is Mollier diagram or psychrometric chart.

The design of the diagram, in principle, can be somewhat different. A typical general scheme of the Id diagram is shown below in Figure 3.1. The diagram is a working field in the oblique coordinate system Id, on which several coordinate grids are plotted and auxiliary scales along the perimeter of the diagram. The moisture content scale is usually located at the bottom edge of the chart, with the constant moisture content lines being vertical straight lines. The lines of constants are parallel straight lines, usually going at an angle of 135° to the vertical moisture content lines (in principle, the angles between the enthalpy and moisture content lines can be different). The oblique coordinate system is chosen in order to increase the working area of ​​the diagram. In such a coordinate system, the lines of constant temperatures are straight lines that run at a slight inclination to the horizontal and slightly fan out.

The working field of the diagram is limited by curved lines of equal relative humidity of 0% and 100%, between which lines of other values ​​of equal relative humidity are plotted with a step of 10%.

The temperature scale is usually located on the left edge of the working field of the chart. The values ​​of air enthalpies are usually plotted under the curve F = 100. The values ​​of partial pressures are sometimes applied along the upper edge of the working field, sometimes along the lower edge under the moisture content scale, sometimes along the right edge. In the latter case, an auxiliary curve of partial pressures is additionally built on the diagram.

Determination of humid air parameters on the Id diagram.

The point on the diagram reflects a certain state of the air, and the line - the process of changing the state. The definition of the parameters of the air, which has a certain state, displayed by point A, is shown in Figure 3.1.