Atmospheric air is almost always humid due to the evaporation of water from open reservoirs into the atmosphere, as well as due to the combustion of organic fuels with the formation of water, etc. Heated atmospheric air is very often used for drying various materials in drying chambers and in other technological processes. The relative content of water vapor in the air is also one of the most important components of climatic comfort in residential premises and in premises for long-term storage. food products and industrial products. These circumstances determine the importance of studying the properties humid air and calculation of drying processes.
Here we will consider the thermodynamic theory of humid air, mainly with the aim of learning how to calculate the drying process of wet material, i.e. learn how to calculate the air flow that would provide the required drying rate of the material for the given parameters of the drying plant, as well as to consider the analysis and calculation of air conditioning and air conditioning installations.
The water vapor that is present in the air can be either superheated or saturated. Under certain conditions, water vapor in the air can condense; then the moisture falls out in the form of fog (cloud), or the surface fogs up - dew falls. Nevertheless, despite the phase transitions, water vapor in moist air can be considered with great accuracy as an ideal gas up to the dry saturated state. Indeed, for example, at a temperature t\u003d 50 ° C saturated water vapor has a pressure ps = 12300 Pa and specific volume. Bearing in mind that the gas constant for water vapor
those. with these parameters, even saturated water vapor with an error of no more than 0.6% behaves like an ideal gas.
Thus, we will consider moist air as a mixture of ideal gases with the only caveat that in states close to saturation, the parameters of water vapor will be determined from tables or diagrams.
Let us introduce some concepts characterizing the state of humid air. Let in the volume of space 1 m 3 there is moist air in an equilibrium state. Then the amount of dry air in this volume will, by definition, be the density of dry air ρ sv (kg / m 3), and the amount of water vapor, respectively, ρ VP (kg / m 3). This amount of water vapor is called absolute humidity humid air. The density of moist air will obviously be
In this case, it should be borne in mind that the densities of dry air and water vapor must be calculated at the corresponding partial pressures, in such a way that
those. we consider Dalton's law to be valid for moist air.
If the temperature of the important air is t, then
Often instead of water vapor density, i.e. instead of absolute humidity, humid air is characterized by the so-called moisture content d, which is defined as the amount of water vapor per 1 kg of dry air. To determine the moisture content d allocate some volume in moist air V 1, such that the mass of dry air in it is 1 kg, i.e. dimension V 1 in our case there is m 3 / kg St. Then the amount of moisture in this volume will be d kg VP / kg St. It is clear that the moisture content d associated with the absolute humidity ρ vp. In fact, the mass of moist air in volume V 1 equals
But since the volume V 1 we chose so that it contained 1 kg of dry air, then obviously . The second term is, by definition, moisture content d, i.e.
Considering dry air and water vapor as ideal gases, we get
Taking into account, we find the relationship between moisture content and the partial pressure of water vapor in the air
Substituting here the numerical values , we finally have
Since water vapor is still not an ideal gas in the sense that its partial pressure and temperature are much lower than the critical ones, humid air cannot contain an arbitrary amount of moisture in the form of vapor. Let's illustrate this with a diagram. p–v water vapor (see Fig. 1).
Let the initial state of water vapor in moist air be represented by point C. If now at a constant temperature t With the addition of moisture in the form of steam to moist air, for example, by evaporating water from an open surface, the point representing the state of water vapor will move along the isotherm t C = const to the left. The density of water vapor in moist air, i.e. its absolute humidity will increase. This increase in absolute humidity will continue until water vapor at a given temperature t C will not become dry saturated (state S). A further increase in absolute humidity at a given temperature is impossible, since water vapor will begin to condense. Thus, the maximum value of absolute humidity at a given temperature is the density of dry saturated steam at this temperature, i.e.
The ratio of absolute humidity at a given temperature and the maximum possible absolute humidity at the same temperature is called the relative humidity of moist air, i.e. by definition we have
Another variant of vapor condensation in humid air is also possible, namely, isobaric cooling of humid air. Then the partial pressure of water vapor in the air remains constant. Point C on the diagram p–v will shift to the left along the isobar up to the point R. Further, moisture will begin to fall. This situation very often occurs during the summer during the night when the air cools, when dew falls on cold surfaces and fog forms in the air. For this reason, the temperature at point R at which dew begins to fall is called the dew point and is denoted t R. It is defined as the saturation temperature corresponding to a given partial vapor pressure
The enthalpy of moist air per 1 kg of dry air is calculated by summing
it is taken into account that the enthalpies of dry air and water vapor are measured from a temperature of 0 o C (more precisely, from the temperature of the triple point of water, equal to 0.01 o C).
Atmospheric air is a mixture of gases (nitrogen, oxygen, noble gases, etc.) with some water vapor. The amount of water vapor contained in the air is of great importance for the processes occurring in the atmosphere.
Wet air- a mixture of dry air and water vapor. Knowledge of its properties is necessary for understanding and calculating such technical devices as dryers, heating and ventilation systems, etc.
Moist air containing maximum amount water vapor at a given temperature is called rich. Air that does not contain the maximum amount of water vapor possible at a given temperature is called unsaturated. Unsaturated moist air consists of a mixture of dry air and superheated water vapor, while saturated moist air consists of dry air and saturated water vapor. Water vapor is contained in the air, usually in small quantities and in most cases in a superheated state, so the laws of ideal gases apply to it.
Humid air pressure AT, according to Dalton's law, is equal to the sum of the partial pressures of dry air and water vapor:
B = p B + p P, (2.1)
where AT– barometric pressure, Pa, p B, r P are the partial pressures of dry air and water vapor, respectively, Pa.
In the process of isobaric cooling of unsaturated moist air, a state of saturation can be reached. The condensation of water vapor contained in the air, the formation of fog indicate the achievement dew points or dew temperature. The dew point is the temperature to which moist air must be cooled at constant pressure to become saturated.
The dew point depends on the relative humidity of the air. At high relative humidity, the dew point is close to the actual air temperature.
Absolute humidity ρ P determines the mass of water vapor contained in 1 m 3 of moist air.
Relative humidity φ determines the degree of air saturation with water vapor:
those. actual absolute humidity ratio ρ P to the highest possible absolute humidity in saturated air ρ N at the same temperature.
For saturated air φ = 1 or 100%, and for unsaturated moist air φ < 1.
The value of moisture content, expressed in terms of partial pressures:
(2.4)
As can be seen from equation (2.4), with increasing partial pressure r P moisture content d increases.
The enthalpy of humid air is one of its main parameters and is widely used in the calculations of drying plants, ventilation and air conditioning systems. The enthalpy of moist air is related to a unit mass of dry air (1 kg) and is defined as the sum of the enthalpies of dry air i B and water vapor i P, kJ/kg:
i = i B + i P ∙d(2.5)
id - diagram of humid air
id- the humid air diagram was proposed in 1918. prof. OK. Ramzin. In the diagram (Fig. 2.1), the abscissa shows the values of moisture content d, g/kg, and along the y-axis - enthalpy i moist air, kJ/kg, referred to 1 kg of dry air. For better use of line chart area i=const drawn at an angle of 135° to the lines d=const and values d moved to a horizontal line. Isotherms ( t=const) are plotted as straight lines.
By id– In the humid air diagram, for each state of humid air, the dew point temperature can be determined. To do this, from a point characterizing the state of the air, it is necessary to draw a vertical (line d=const) before crossing the line φ =100%. The isotherm passing through the obtained point will determine the desired dew point of moist air.
saturation curve φ =100% shared id- a diagram for the upper region of unsaturated moist air and the lower region of supersaturated air, in which moisture is in a droplet state (fog region).
id- the diagram can be used to solve problems related to the drying of materials. The drying process consists of two processes: heating moist air and moistening it, due to the evaporation of moisture from the dried material.
Rice. 2.1. id– diagram of humid air
heating process proceeds at a constant moisture content ( d=const) and displayed on id- diagram with a vertical line 1-2 (Fig. 2.1). The enthalpy difference in the diagram determines the amount of heat consumed to heat 1 kg of dry air:
Q = M B∙(i 2 - i 1), (2.6)
Ideal saturation process air moisture in the drying chamber occurs at a constant enthalpy ( i=const) and is shown as a straight line 2-3′. The difference in moisture content gives the amount of moisture released in the drying chamber by each kilogram of air:
M P \u003d M V∙(d 3 - d 2), (2.7)
The actual drying process is accompanied by a decrease in enthalpy, i.e. i≠const and is drawn straight 2-3 .
REAL GASES
Ministry of Education and Science of the Russian Federation
Federal Agency for Education
Saratov State Technical University
DETERMINATION OF HUMID AIR PARAMETERS
Guidelines
for students of specialties 280201
full-time and part-time education
Saratov 2009
Objective: deepening knowledge in the section of technical thermodynamics "Humid air", studying the methodology for calculating the parameters of humid air and gaining skills in working with measuring instruments.
As a result of the work should be learned:
1) basic concepts of humid air;
2) a method for determining the parameters of moist air according to
calculated dependencies;
3) a method for determining the parameters of moist air according to
I-d-diagram.
1) determine the value of the parameters of moist air according to
calculated dependencies;
2) determine the parameters of humid air using
I-d-diagrams;
3) draw up a report on the performed laboratory work.
BASIC CONCEPTS
Air that does not contain water vapor is called dry air. Dry air does not occur in nature, since atmospheric air always contains some water vapor.
A mixture of dry air and water vapor is called moist air. Humid air is widely used in drying and ventilation installations, air conditioning devices, etc.
A characteristic feature of the processes occurring in humid air is that the amount of water vapor contained in the air changes. Steam can partially condense and, conversely, water evaporates into the air.
A mixture of dry air and superheated water vapor is called unsaturated moist air. The partial vapor pressure pp in the mixture is less than the saturation pressure p, corresponding to the temperature of moist air (pp<рн). Температура пара выше температуры его насыщения при данном парциальном давлении.
A mixture of dry air and dry saturated water vapor is called saturated moist air. The partial pressure of water vapor in the mixture is equal to the saturation pressure corresponding to the temperature of moist air. The vapor temperature is equal to the condensation temperature at a given partial vapor pressure.
A mixture consisting of dry air and moist saturated water vapor (that is, there are particles of condensed vapor in the air that are in suspension and fall out in the form of dew) is called supersaturated humid air. The partial pressure of water vapor is equal to the saturation pressure corresponding to the temperature of moist air, which in this case is equal to the condensation temperature of the steam in it. In this case, the temperature of moist air is called the dew point temperature. tR. If, for some reason, the partial pressure of water vapor turns out to be greater than the saturation pressure, then part of the vapor will condense in the form of dew.
The main indicators characterizing the state of moist air are moisture content d, relative humidity j, enthalpy I and density r.
The parameters of moist air are calculated using the Mendeleev-Clapeyron equation for an ideal gas, to which moist air obeys with sufficient approximation. Consider moist air as a gas mixture consisting of dry air and water vapor.
According to Dalton's law, the pressure of moist air R equals:
where rv- partial pressure of dry air, Pa;
rp- partial pressure of water vapor, Pa.
The maximum value of the partial pressure of water vapor is equal to the pressure of saturated water vapor pH, corresponding to the temperature of humid air.
The amount of water vapor in a mixture in kg per 1 kg of dry air is called moisture content d, kg/kg:
https://pandia.ru/text/78/602/images/image003_38.gif" width="96" height="53">, since then ; (3)
Since , then , (4)
where V is the volume of the gas mixture, m3;
Rin, RP are the gas constants of air and water vapor, equal to
Rin=287 J/(kg×K), RP=461 J/(kg×K);
T is the temperature of humid air, K.
Given that 
, and, substituting expressions (3) and (4) into formula (2), we finally obtain:
DIV_ADBLOCK64">
relative humidity j called the ratio of vapor density (i.e. absolute humidity rP) to the maximum possible absolute humidity (density rPmax) at a given temperature and pressure of moist air:
As rP and rPmax determined at the same temperature of moist air, then
https://pandia.ru/text/78/602/images/image013_6.gif" width="107" height="31"> . (8)
The density of dry air and water vapor is determined from the Mendeleev-Clapeyron equation, written for these two components of the gas mixture according to (3) and (4).
R is found according to the formula:
https://pandia.ru/text/78/602/images/image015_6.gif" width="175" height="64 src=">.
Enthalpy of moist air I is the sum of the enthalpies of 1 kg of dry air and d kg of water vapor:
I= iin+ d× iP . (11)
Enthalpy of dry air and steam:
https://pandia.ru/text/78/602/images/image017_4.gif" width="181" height="39"> , (13)
where tm– wet bulb readings, °С;
(tc- tm) – psychrometric difference, °C;
X– correction to the wet bulb temperature, %, is determined
according to the schedule located on the stand, depending on tm and speed
A barometer is used to determine the pressure of moist air.
PROCEDURE AND PROCESSING TECHNIQUE
EXPERIMENTAL RESULTS
Measure dry and wet bulb temperatures. Determine the true value of the wet bulb temperature using formula (13). Find difference Dt = tc - tm ist and according to the psychrometric table to determine the relative humidity of the air.
Knowing the value of relative humidity, from expression (7) find the partial pressure of water vapor.
according to (12), (13).
The specific volume of moist air is found by the formula:
Mass of moist air M, kg, in the laboratory room is determined by the formula:
where V– room volume, m3;
R– pressure of humid air, Pa.
Enter the results of calculations and instrument readings in the table in the following form.
Protocol for recording readings of measuring instruments
and calculation results
Name of the quantity to be determined | Designation | Dimension | numerical magnitude |
|
Humid air pressure | ||||
Dry bulb temperature | ||||
Wet bulb temperature | tm | |||
Relative humidity | ||||
Saturated steam pressure | ||||
Partial pressure of water vapor | ||||
Partial pressure of dry air | ||||
Density of moist air | ||||
Absolute humidity | rP | |||
Gas constant of humid air | ||||
Enthalpy of moist air | ||||
Moist air mass |
Next, you should determine the main parameters of moist air according to the measured tc and tm using the I-d diagram. The intersection point on the I-d-diagram of isotherms corresponding to the temperatures of wet and dry bulbs characterizes the state of humid air.
Compare the data obtained from the I-d-diagram with the values determined using mathematical dependencies.
The maximum possible relative error in determining the partial pressure of water vapor and dry air is determined by the formulas:
https://pandia.ru/text/78/602/images/image022_2.gif" width="137" height="51">; 
,
where D denotes the limit of the absolute measurement error
The absolute error limit of the hygrometer in this lab is ±6%. The absolute permissible error of the thermometers of the psychrometer is ±0.2%. A barometer with an accuracy class of 1.0 is installed in the work.
WORK REPORT
The report on the performed laboratory work should contain
following:
1) short description work;
2) protocol for recording the readings of measuring instruments and
calculation results;
3) drawing with I-d-diagram, where the state of wet is determined
air in this experiment.
TEST QUESTIONS
1. What is called moist air?
2. What is called saturated and unsaturated moist air?
3. Dalton's law as applied to moist air.
4. What is the dew point temperature?
5. What is called absolute humidity?
6. What is called the moisture content of moist air?
7. To what extent can the moisture content change?
8. What is called relative humidity?
9. In the I-d diagram, show the lines j=const, I=const; d=const, tс=const, tm=const.
10. What is the maximum possible vapor density at a given temperature of moist air?
11. What determines the maximum possible partial pressure of water vapor in moist air and what is it equal to?
12. On what parameters of humid air does the temperature of a wet bulb depend and how does it change when they change?
13. How can the partial pressure of water vapor in a mixture be determined if the relative humidity and temperature of the mixture are known?
14. Write the Mendeleev-Clapeyron equation for dry air, water vapor, moist air and explain all the quantities included in the equation.
15. How to determine the density of dry air?
16. How to determine the gas constant and the enthalpy of moist air?
LITERATURE
1. Lyashkov fundamentals of heat engineering /. M.: graduate School, 20s.
2. Zubarev on technical thermodynamics /,. M.: Energy, 19s.
DETERMINATION OF HUMID AIR PARAMETERS
Guidelines for performing laboratory work
on the courses "Heat engineering", "Technical thermodynamics and heat engineering"
Compiled by: SEDELKIN Valentin Mikhailovich
KULESHOV Oleg Yurievich
KAZANTSEVA Irina Leonidovna
Reviewer
Editor
License ID No. 000 dated 11/14/01
Signed for printing Format 60x84 1/16
Boom. type. Condition-print. l. Uch.-ed. l.
Circulation copies. Order Free
Saratov State Technical University
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The air around us is a mixture of gases. It is almost always wet. Water vapor, unlike other components of the mixture, can be in the air, both in a superheated and in a saturated state. The content of water vapor in the air changes, both in the process of its moisture treatment in supply ventilation systems and air conditioners, and during the assimilation of moisture emissions by air in the room. The dry part of moist air usually contains (by volume): about 75% nitrogen, 21% oxygen, 0.03% carbon dioxide and a small amount of inert gases - argon, neon, helium, xenon, krypton), hydrogen, ozone and others. The specified components of the gas mixture of air constitute its dry part, the other part air mass it's water vapor.
Air is treated as mixture of ideal gases, which allows using the laws of thermodynamics to obtain calculation formulas.
According to Dalton's law, each gas of a mixture that makes up air occupies its own volume, has its own partial pressure.
Pi ,
and has the same temperature with other gases of this mixture.
Attention! Important definition:
The sum of the partial pressures of each of the components of the mixture is equal to the total barometric pressure of the air.
B = Σ R i , Pa.
Consider the concept of what is partial pressure ?
Partial pressure- this is the pressure that the gas that is part of this mixture would have if it were in the same quantity, in the same volume and at the same temperature as in the mixture.
In ventilation calculations, we consider moist air as a binary mixture, i.e. mixture of two gases, which consists of water vapor and dry air. We conditionally accept the dry part of the air as a homogeneous gas.
Thus, barometric pressure equal to the sum of the partial pressures of dry air P r.v. and water vapor P p , i.e.,
B = P r.v. +P p
Under normal indoor conditions, when the water vapor pressure R p approximately equal to 15 mm. rt. Art., share of the second member P r.v. in the barometric pressure formula, taking into account the difference in the density of moist and dry air, ceteris paribus is only 0.75% of the density of dry air ρ r.v. . Therefore, in our engineering calculations, it is assumed that
ρ air. = ρ r.v.
ρ air. = ρ r.v.
When the air humidity changes in ventilation processes, the mass of its dry part remains unchanged. Based on this, it is customary to attribute the mass of water vapor contained in the air to 1 kg. dry part of the air.
Let's go directly to those physical quantities that determine the parameters of moist air. It is the combination of these parameters that determines the state of moist air:
is a value that characterizes degree of body heat. It is a measure of the average kinetic energy of the translational motion of molecules. Currently, the Celsius temperature scale and the Kelvin thermodynamic temperature scale, which is based on the second law of thermodynamics, are used. Between temperatures expressed in degrees Kelvin and degrees Celsius, there is a relationship, namely:
T, K = 273.15 + t °C
It is important to note that the state parameter is the absolute temperature expressed in Kelvin, but the degree of the absolute scale is numerically equal to the Celsius degree, i.e.
dT = dt.
Air humidity is characterized by the mass of water vapor contained in it. The mass of water vapor in grams per 1 kg of the dry part of moist air is called air moisture content d, g/kg.
Value d is equal to:
where: B
- barometric pressure, equal to the sum of the partial pressures of dry air.
P r.v.
and water vapor P p
;
P p
is the partial pressure of water vapor in unsaturated moist air.
Value φ equal to the ratio of the partial pressure of water vapor in unsaturated moist air P p. to the partial pressure of water vapor in saturated moist air P n.p. at the same temperature and barometric pressure, i.e.,
At a relative humidity of 100%, the air is completely saturated with water vapor, and it is called saturated with moist air , and the water vapor contained in this air is in a saturated state.
If a φ < 100%, then the air contains water vapor in a superheated state and it is called unsaturated moist air .
The pressure of saturated water vapor depends only on temperature. Its value is determined experimentally and given in special tables. There are a number of formulas approximating the dependence Pn.p. in Pa or in mm. rt. st. from temperature in t °C.
For example, for the region of positive temperatures from 0°C and above the pressure of saturated water vapor in Pa, approximately expressed by the dependence:
P n.p. \u003d 479 + (11.52 + 1.62 t) 2, Pa
Using the concept of relative humidity φ , the moisture content of the air can be defined as
For ventilation processes, the temperature range is a constant value and is equal to
From r.v. = 1.005 kJ/(kg ×°C).
In normal ventilation processes in the temperature range, this value can be considered constant and equal to
C p = 1.8 kJ/(kg × °C).
J r.v. = C r.v. × t ,
where: t is the air temperature, in °C.
Dry air enthalpy J r.v. at t = 0°C are taken equal to 0.
for water at t = 0°C is equal to 2500 kJ/kg.
in air at an arbitrary temperature t, is
J p \u003d 2500 + 1.8 t.
consists of the enthalpy of its dry part and the enthalpy of water vapor.
Enthalpy J humid air, referred to 1 kg dry part of moist air kJ/kg, at an arbitrary temperature t and arbitrary moisture content d, is equal to:
where: 1,005
– C r.v. heat capacity of dry air, _kJ/(kg×°С);
2500
– r specific heat of vaporization, kJ/(kg×°С);
1,8
– C p heat capacity of water vapor, kJ/(kg×°С).
If air carries sheer warmth, it heats up, i.e. its temperature rises. When moist air is heated, the enthalpy changes as a result of a change in the temperature of the dry part of the air and water vapor. When water vapor with the same temperature enters the air from external sources (isothermal steam humidification), latent heat vaporization. The enthalpy of moist air also increases, because the enthalpy of water vapor is added to the enthalpy of the dry part of the air. At the same time, the air temperature almost does not change, which was the reason for the introduction of this term - latent heat.
In general, the enthalpy of humid air is made up of sensible and latent heat, which is why enthalpy is sometimes referred to as total heat.
For further calculations of ventilation and air conditioning systems, we need the following basic parameters of humid air:
- temperature t in , °C ;
- moisture content d in , g/kg ;
- relative humidity φ in , % ;
- heat content J in , kJ/kg ;
- concentration of harmful impurities With , mg / m 3 ;
- movement speed V in , m/sec.
Rice. 1. Display of air treatment processes on d-h-diagram
Rice. 2. Image on the d-h-diagram of air parameters during conditioning
Basic terms and definitions
Atmospheric air is a non-separable mixture of gases (N2, O2, Ar, CO2, etc.), which is called dry air, and water vapor. The air condition is characterized by: temperature t [°C] or T [K], barometric pressure rb [Pa], absolute rabs = rb + 1 [bar] or partial ppar, density ρ [kg/m3], specific enthalpy (heat content) h [kJ/kg]. The state of moisture in atmospheric air is characterized by absolute humidity D [kg], relative humidity ϕ [%] or moisture content d [g / kg]. Atmospheric air pressure pb is the sum of the partial pressures of dry air pc and water vapor pp (Dalton's law):
rb = rs + rp. (one)
If gases can be mixed in any quantities, then air can only contain a certain amount of water vapor, because the partial pressure of water vapor in the mixture cannot be greater than the partial saturation pressure p of these vapors at a given temperature. The existence of a limiting partial saturation pressure is manifested in the fact that all excess water vapor in excess of this amount condenses.
In this case, moisture can fall out in the form of water droplets, ice crystals, fog or frost. The smallest amount of moisture in the air can be reduced to zero (at low temperatures), and the highest - about 3% by mass or 4% by volume. Absolute humidity D is the amount of steam [kg] contained in one cubic meter of moist air:
where Mn is the mass of steam, kg; L is the volume of humid air, m3. In practical calculations, the unit of measurement characterizing the vapor content in humid air is taken to be the moisture content. Moisture content of humid air d is the amount of steam contained in the volume of humid air, consisting of 1 kg of dry air and Mv [g] of steam:
d = 1000(Mp/Mc), (3)
where Mc is the mass of the dry part of moist air, kg. Relative humidity ϕ or degree of humidity, or hygrometric index, is the ratio of the partial pressure of water vapor to the partial pressure of saturated vapor, expressed as a percentage:
ϕ = (rp/pn)100% ≈ (d/dp)100%. (4)
Relative humidity can be determined by measuring the rate of evaporation of water. Naturally, the lower the humidity, the more actively the evaporation of moisture will occur. If the thermometer is wrapped with a damp cloth, then the readings of the thermometer will decrease relative to the dry bulb. The difference between the temperature readings of dry and wet thermometers gives a certain value of the degree of humidity of atmospheric air.
The specific heat capacity of air, c, is the amount of heat required to heat 1 kg of air by 1 K. The specific heat capacity of dry air at constant pressure depends on temperature, but for practical calculations of SCR systems, the specific heat capacity of both dry and moist air is:
ss.w = 1 kJ/(kg⋅K) = 0.24 kcal/(kg⋅K) = 0.28 W/(kg⋅K), (5)
The specific heat capacity of water vapor cp is taken equal to:
cn = 1.86 kJ/(kg⋅K) = 0.44 kcal/(kg⋅K) = 0.52 W/(kg⋅K), (6)
Dry or sensible heat is heat that is added to or removed from air without changing the state of aggregation of the vapor (temperature changes). Latent heat is the heat used to change the state of aggregation of steam without changing the temperature (for example, drying).
Otherwise, this is the amount of heat that is necessary to heat from zero to a given temperature such an amount of air, the dry part of which is 1 kg. Usually, the specific enthalpy of air is taken h = 0 at air temperature t = 0 and moisture content d = 0. The enthalpy of dry air hc.v is equal to:
hc.v = ct = 1.006t [kJ/kg], (7)
where c is the specific heat capacity of air, kJ / (kg⋅K). The enthalpy of 1 kg of water vapor is:
hv.p = 2500 + 1.86t [kJ/kg], (8)
where 2500 is the latent heat of vaporization of 1 kg of water at a temperature of zero degrees, kJ/kg; 1.86 is the heat capacity of water vapor, kJ / (kg⋅K). At the temperature of moist air t and moisture content d, the enthalpy of moist air is equal to:
hv.v = 1.006t + (2500 +1.86t)×(d/1000) [kJ/kg], where d = (ϕ/1000)dn [g/kg], (9)
The heat and cooling capacity Q of an air conditioning system can be determined by the formula:
Q = m(h2 - h1) [kJ/h], (10)
where m is air consumption, kg; h1, h2 are the initial and final enthalpies of air. If moist air is cooled at a constant moisture content, the enthalpy and temperature will decrease, and the relative humidity will increase. There will come a moment when the air becomes saturated and its relative humidity will be equal to 100%. This will begin the evaporation of moisture from the air in the form of dew - vapor condensation.
This temperature is called the dew point. The dew point temperature for various dry air temperatures and relative humidity is given in Table. 1. The dew point is the limit of how humid air can be cooled at a constant moisture content. To determine the dew point, it is necessary to find such a temperature at which the moisture content of air d will be equal to its moisture capacity dн.
Graphical construction of air treatment processes
To facilitate calculations, the equation for the heat content of moist air is presented in the form of a graph called the d-h diagram (the term i-d diagram is sometimes used in the technical literature). In 1918, Professor of St. Petersburg University L.K. Ramzin proposed a d-diagram, which unambiguously reflects the relationship between the parameters of moist air t, d, h, ϕ at a certain atmospheric pressure pb.
With the help of the d-h diagram, the graphical method simply solves problems, the solution of which analytically requires, albeit simple, but painstaking calculations. In the technical literature, there are various interpretations of this diagram, which have minor differences from Ramzin's d-h diagram.
These are, for example, the Mollier diagram, the Carrier diagram published by the American Society for Heating, Refrigeration and Air Conditioning (ASHRAE), the diagram of the French Association of Climate, Ventilation and Refrigeration Engineers (AICVF). The last chart is very accurate, printed in three colors.
However, in our country, the Ramzin diagram was distributed and is currently used, as a rule. It is available in many textbooks, it is used by design organizations. Therefore, we also took it as a basis (Fig. 1). This Ramzin d-h diagram is built in an oblique coordinate system. The values of enthalpy h are plotted along the ordinate axis, and the moisture content d is plotted along the abscissa axis, located at an angle of 135 ° to the ordinate axis. The origin of coordinates (point 0) corresponds to the values h = d = 0.
Below point 0, negative values of enthalpy are plotted, above - positive ones. On the grid obtained in this way, lines of isotherms t = const, lines of constant relative humidity ϕ = const, partial pressure of water vapor and moisture content are plotted. The lower curve ϕ = 100% characterizes the saturated state of the air and is called the boundary curve. When the barometric pressure increases, the saturation line moves up, and when the pressure decreases, it moves down.
Thus, when performing calculations for SLE located in the area of Kyiv, it is necessary to use a diagram with barometric pressure pb = 745 mm Hg. Art. = 99 kPa. On the d-h diagram, the area above the boundary curve (ϕ = 100%) is the area of unsaturated steam, and the area below the boundary curve is supersaturated moist air.
In this region, saturated air contains moisture in the liquid or solid phase. As a rule, this state of air is unstable; therefore, the processes in it are not considered on the d-h diagram. On the d-h diagram, each point above the boundary curve reflects a certain state of the air (temperature, moisture content, relative humidity, enthalpy, partial pressure of water vapor).
If the air undergoes a thermodynamic process, then its transition from one state (point A) to another (point B) corresponds to the line A-B on the d-diagram. In general, this is a curved line. However, we are only interested in the initial and final states of the air, and the intermediate ones do not matter, so the line can be represented as a straight line connecting the initial and final states of the air.
To determine the point on the d-h diagram corresponding to a certain state of air, it is enough to know two parameters that are independent of each other. The desired point is located at the intersection of lines corresponding to these parameters. Having drawn perpendiculars to the lines on which other parameters are plotted, their values are determined. The dew point temperature is also determined on the d-h diagram.
Since the dew point temperature is the lowest temperature to which air can be cooled at a constant moisture content, to find the dew point it is enough to draw the line d = const until it intersects with the curve ϕ = 100%. The point of intersection of these lines is the dew point, and the corresponding temperature is the dew point temperature. Using the d-h diagram, you can determine the air temperature using a wet bulb.
To do this, from a point with given air parameters, we draw an isenthalpe (h = const) until it intersects with the line ϕ = 100%. The temperature corresponding to the point of intersection of these lines is the temperature of the wet bulb. The technical documentation for air conditioners specifies the conditions under which the measurements of the nominal cooling capacity were made. As a rule, this is the temperature of dry and wet bulbs, corresponding to a relative humidity of 50%.
air heating process
When the air is heated, the line of the thermodynamic process runs along the straight line A-B with a constant moisture content (d = const). Air temperature and enthalpy increase and relative humidity decreases. The heat consumption for air heating is equal to the difference between the enthalpies of the final and initial states of the air.
Air cooling process
The process of air cooling on the d-h diagram is reflected by a straight line directed vertically downwards (straight line A-C). The calculation is carried out similarly to the heating process. However, if the cooling line goes below the saturation line, then the cooling process will follow straight A-C and further along the line ϕ = 100% from point C1 to point C2. Point C2 parameters: d = 4.0 g/kg, t = 0.5 °C.
Moist air dehumidification process
Dehumidification of moist air with absorbents without changing the heat content (without heat removal and heat supply) occurs along a straight line h = const, that is, along straight A-D pointing up and to the left (straight line A-D1). At the same time, the moisture content and relative humidity decrease, and the air temperature increases, because. in the process of absorption, vapor condenses on the surface of the absorbent, and the released latent heat of the vapor is converted into sensible heat. The limit of this process is the point of intersection of the line h = const with the ordinate d = 0 (point D1). The air at this point is completely devoid of moisture.
Adiabatic humidification and air cooling
Adiabatic humidification and cooling (without heat exchange with the external environment) on the d-h diagram from the initial state (point N) is reflected by a straight line directed downward along h = const (point K). The process occurs when air comes into contact with water, which is constantly circulating in the reverse cycle. At the same time, the air temperature drops, the moisture content and relative humidity increase.
The process limit is the point on the curve ϕ = 100%, which is the wet bulb temperature. At the same time, the recirculating water must acquire the same temperature. However, in real SCW during adiabatic processes of air cooling and humidification, the point ϕ = 100% is somewhat not reached.
Air mixing with different parameters
On the d-h diagram, the parameters of mixed air (with the parameters corresponding to the points (X and Y) can be obtained as follows. We connect the points X and Y with a straight line. The parameters of the mixed air lie on this straight line, and the Z point divides it into segments inversely proportional to the air mass each of constituent parts. If we denote the proportion of the mixture n = Gx / Gy, then in order to straight X-Y to find the point Z, it is necessary to divide the line X-Y into the number of parts n + 1 and from the point X set aside a segment equal to one part.
The mixture point will always be closer to the parameters of the air, the dry part of which has a large mass. When mixing two volumes of unsaturated air with states corresponding to points X1 and Y1, it may happen that the straight line X1-Y1 crosses the saturation curve ϕ = 100% and point Z1 will be in the fogging area. This position of the mixture point Z2 shows that as a result of mixing, moisture will fall out of the air.
In this case, the mixture point Z1 will move to a more stable state on the saturation curve ϕ = 100% to the point Z2 along the isenthalpe. At the same time, dZ1 - dZ2 grams of moisture falls out for each kilogram of the mixture.
Slope on d-h diagram
Attitude:
ε = (h2 - h1)/(d2 - d1) = ∆h/∆d (11)
uniquely determines the nature of the process of changing moist air. Moreover, the values of Δh and Δd may have a "+" or "-" sign, or they may be equal to zero. The value of ε is called the heat-humidity ratio of the process of changing moist air, and when the process is depicted by a beam on the d-h diagram, it is called the slope coefficient:
ε = 1000(Δh/Δd) = ±(Qg/Mv), kJ/kg,(12)
Thus, the angular coefficient is equal to the ratio of excess heat to the mass of released moisture. The angular coefficient is represented by segments of rays on the frame of the field of the d-h diagram (slope coefficient scale). So, to determine the slope coefficient process X-Z it is necessary to draw a straight line parallel to the X-Z process line from point 0 (on the temperature scale) to the slope scale. In this case O-N line will indicate a slope equal to 9000 kJ/kg.
Thermodynamic model of SCR
The process of preparing air before supplying it to a conditioned room is a set of technological operations and is called air conditioning technology. The technology of heat and moisture treatment of conditioned air is determined by the initial parameters of the air supplied to the air conditioner and the required (set) parameters of the air in the room.
To select air treatment methods, a d-h diagram is built, which allows, under certain initial data, to find a technology that will provide the specified air parameters in the serviced room with minimal energy, water, air, etc. consumption. The graphical display of air treatment processes on a d-h diagram is called a thermodynamic model of an air conditioning system (TDM).
The parameters of the outside air supplied to the air conditioner for further processing vary throughout the year and day in a wide range. Therefore, we can speak of outdoor air as a multidimensional function Xн = хн(t). Accordingly, the set of supply air parameters is a multidimensional function Xpr = xpr(t), and in the manned room Xpm = xpm(t) (parameters in the working area).
A technological process is an analytical or graphical description of the process of movement of a multidimensional function Xн to Xpr and further to Xp. Note that the variable state of the system x(ϕ) refers to the generalized indicators of the system at various points in space and at various points in time. The thermodynamic model of the movement of the function Xn to Xp is built on the d-h diagram, and then the air treatment algorithm, the necessary equipment and the method for automatically controlling air parameters are determined.
The construction of TDM begins with drawing on the d-h diagram of the state of the outdoor air of a given geographical point. The design area of possible states of the outside air is taken according to SNiP 2.04.05-91 (parameters B). The upper limit is the isotherm tl and isoenthalpe hl (limiting parameters of the warm period of the year). The lower limit is the isotherm tsm and isoenthalpe hzm (limiting parameters of cold and transition periods of the year).
The limit values for the relative humidity of the outdoor air are taken based on the results of meteorological observations. In the absence of data, the range from 20 to 100% is taken. Thus, the multidimensional function of possible outdoor air parameters is contained in the polygon abcdefg (Fig. 2). Then the required (calculated) value of the state of the air in the room or in the working area is applied to the d-h diagram.
This can be a point (precision air conditioning) or a work area P1P2P3P4 (comfort air conditioning). Next, the angular coefficient of change in the parameters of the air in the room ε is determined and the process lines are drawn through the boundary points of the working area. In the absence of data on the heat and humidity process in the room, it can be approximately taken in kJ / kg: trade enterprises and Catering- 8500-10000; auditoriums - 8500-10000; apartments - 15000-17000; office space - 17000-20000.
After that, a zone of supply air parameters is built. To do this, on the lines ε drawn from the boundary points of the P1P2P3P4 zone, segments are plotted corresponding to the calculated temperature difference:
Δt = tmo - tpr, (13)
where tpr is the calculated supply air temperature. The solution of the problem is reduced to the transfer of air parameters from the multidimensional function Xn to the function Xpm. The value of Δt is taken according to the norms or calculated based on the parameters of the refrigeration system. For example, when using water as a coolant, the final water temperature in the spray chamber tw will be:
tw = t2 + Δt1 + Δt2 + Δt3, (14)
where t1 is the water temperature at the outlet of the chiller (5-7 °C); Δt1 is the rise in water temperature in the pipeline from the chiller to the water heat exchanger of the air conditioner (1 °C); Δt2 - water heating in the irrigation chamber (2-3 °С); Δt3 - water heating due to the bypass coefficient (1°C). Thus, the temperature of the water in contact with air will be tw = 9-12 °C. In practice, air humidity reaches no more than ϕ = 95%, which increases tw to 10-13 °C. The supply air temperature will be:
tw = t2 + Δt2 + Δt3 + Δt4, (15)
where Δt4 is air heating in the fan (1-2 °С); Δt5 - air heating in the supply air duct (1-2 °С). Thus, the supply air temperature will be 12-17 °С. The allowable temperature difference between the removed and supply air Δt for industrial premises is 6-9 °С, for trading floors - 4-10 °С, and with a room height of more than 3 m - 12-14 °С.
In general, the parameters of the air removed from the room differ from the parameters of the air in the working area. The difference between them depends on the method of supplying air to the room, the height of the room, the frequency of air exchange and other factors. Zones U, P and R on the d-h diagram have the same shape and are located along the line ε at distances corresponding to temperature differences: Δt1 = tpom - tpr and Δt2 = tsp - tpom The ratio between tpr, tpom and t is estimated by the coefficient:
m1 = (tpom - tpr)/(tsp - tpr) = (hpom - hpr)/(husp - hpr),(16)
Thus, the air conditioning process is reduced to bringing the set of outdoor air parameters (polygon abcdef) to the allowable set of supply air parameters (polygon P1P2P3P4). When designing, as a rule, electronic d-h charts, various variants of which can be found on the Internet.
One of the common diagrams is the diagram developed by Daichi (Moscow), www.daichi.ru. Using this diagram, you can find the parameters of humid air at different barometric pressures, build process lines, determine the parameters of the mixture of two air flows, etc. reviewed in subsequent issues of our journal.
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