Lecture DRYING.
Drying is the process of removing moisture from solids by evaporating it and removing the resulting vapors.
Heat drying is often preceded mechanical methods removal of moisture (squeezing, settling, filtering, centrifugation).
In all cases, when drying in the form of vapor, a highly volatile component (water, organic solvent, etc.) is removed.
In its physical essence, drying is a process of combined heat and mass transfer and comes down to the movement of moisture under the influence of heat from the depths of the material being dried to its surface and its subsequent evaporation. In the process of drying, a wet body tends to a state of equilibrium with environment, therefore, its temperature and moisture content in the general case are a function of time and coordinates.
In practice the concept is used humidity v, which is defined as:
(5.2)
If then
According to the method of heat supply, they are distinguished:
Convective drying, carried out by direct contact of the material and the drying agent;
Contact (conductive) drying, heat is transferred to the material through the wall separating them;
Radiation drying - by transferring heat by infrared radiation;
Freeze drying, in which moisture is removed from the material while frozen (usually in a vacuum);
Dielectric drying, in which the material is dried in a field of high frequency currents.
With any drying method, the material is in contact with moist air. In most cases, water is removed from the material, so a dry air–water vapor system is usually considered.
Options humid air.
A mixture of dry air and water vapor is moist air. Humid air parameters:
Relative and absolute humidity;
Heat capacity and enthalpy.
Humid air, at low P And T, can be considered a binary mixture of ideal gases - dry air and water vapor. Then, according to Dalton's law, we can write:
(5.3)
Where P– pressure of the vapor-gas mixture , p c g– partial pressure of dry air, – partial pressure of water vapor.
Free or superheated steam - subject to data T&R it does not condense. The maximum possible vapor content in a gas, above which condensation is observed, corresponds to saturation conditions at a certain T and partial pressure .
Distinguish absolute, relative humidity and moisture content of air.
Absolute humidity is the mass of water vapor per unit volume of moist air (kg/m3). The concept of absolute humidity coincides with the concept of vapor density at temperature T and partial pressure .
Relative humidity- this is the ratio of the amount of water vapor in the air to the maximum possible, under given conditions, or the ratio of vapor density under given conditions to the density of saturated vapor under the same conditions:
According to the equation of state of an ideal Mendeleev–Cliperon gas for steam in a free and saturated state, we have:
And 
(5.5)
Here M p is the mass of one mole of vapor in kg, R is the gas constant.
Taking into account (5.5), equation (5.4) takes the form:
Relative humidity determines the moisture content of the drying agent (air).
Here G P– mass (mass flow) of steam, L – mass (mass flow) of absolutely dry gas. Let us express the values of G P and L through the equation of state of an ideal gas:
, 
Then relation (5.7) is transformed to the form:
(5.8)
Mass of 1 mole of dry air in kg.
Introducing 
and considering 
we get:
(5.9)
For the air-water vapor system 
, 
. Then we have:
(5.10)
So, a connection has been established between the moisture content x and the relative humidity φ of the air.
Specific heat of wet gas is taken as the additive value of the heat capacities of dry gas and steam.
Specific heat capacity of wet gas c, referred to 1 kg of dry gas (air):
(5.11)
where is the specific heat capacity of dry gas, the specific heat capacity of steam.
Specific heat capacity, divided by 1 kg vapor-gas mixture:
(5.12)
In calculations they usually use With.
Specific enthalpy of moist air H refers to 1 kg of absolutely dry air and is determined at a given air temperature T as the sum of the enthalpies of absolutely dry air and water vapor:
(5.13)
The specific enthalpy of superheated steam is determined by the following expression.
Humid air called a mixture of dry air and water vapor. Actually atmospheric air always contains some amount of water vapor, i.e. is wet.
Water vapor contained in the air is usually in a rarefied state and obeys the laws for an ideal gas, which allows these laws to be applied to moist air.
State of steam in the air (overheated or saturated) is determined by the value of its partial pressure p, which depends on the total pressure of moist air p and partial pressure of dry air p:
Saturated air– air with the maximum content of water vapor at a given temperature.
Absolute air humidity– mass of water vapor contained
in 1 m moist air (vapor density) at its partial pressure and temperature of moist air:
Relative humidity– the ratio of the actual absolute air humidity to the absolute humidity of saturated air at the same temperature:
At a constant temperature, air pressure changes in proportion to its density (Boyle-Mariotte law), so the relative air humidity can also be determined by the equation:
Where p– air saturation pressure at a given temperature;
p– partial pressure of steam at a given temperature:
For dry air = 0, for saturated air – = 100%.
Dew point- temperature t, at which the steam pressure p becomes equal to the saturation pressure p. When air is cooled below the dew point, water vapor condenses.
air (11.5)
Using the equation of state of an ideal gas for the components of moist air (steam and dry air), dependencies (11.2), (11.3) and (11.5), as well as the molecular masses of air ( = 28.97) and steam ( = 18.016), we obtain the calculation formula :
air (11.6)
For the case when humid air is at atmospheric pressure,: p=B.
Heat capacity of moist air at constant pressure is determined as the sum of heat capacities 1 kg dry air and d, kg water vapor:
(11.7)
In calculations you can take: 
Enthalpy of moist air at a temperature t is defined as the sum of enthalpies 1 kg dry air and d, kg water vapor:
Here r– latent heat of vaporization, equal to ~2500 kJ/kg. Thus, the calculated dependence for determining the value of the enthalpy of moist air takes the form:
(11.9)
Note: magnitude I refers to 1 kg dry air or to (1+ d) kg humid air.
In technical calculations, to determine the parameters of humid air, it is usually used I–d humid air diagram proposed in 1918 by Professor L.K. Ramzin.
IN I–d The diagram (see Fig. 11.2) graphically relates the main parameters that determine the thermal and humidity state of the air: temperature t, relative air humidity, moisture content d, enthalpy I, partial pressure of steam P contained in the steam-air mixture. Knowing any two parameters, you can find the rest at the intersection of the corresponding
lines I–d-diagrams.
2. Scheme of the laboratory setup ( device )
Relative humidity in laboratory work determined using a psychrometer of the type: "Psychrometric hygrometer VIT-1".
The psychrometer (Fig. 11.1) consists of two identical thermometers:
“dry” – 1 and “wet” – 2. Wetting of the thermometer ball 2 is carried out using a cambric wick 3, lowered into a vessel 4 with water.
2 1
 |
3 t
 |
4t and air humidity φ for this device was established experimentally. Based on the results of the experiments, a special psychrometric table (passport) was compiled and placed on the front panel of the laboratory psychrometer.
The rate of evaporation is significantly influenced by the speed of air flow around the cambric wick, which introduces an error in the readings of a conventional psychrometer. This error is taken into account in the calculations by introducing corrections in accordance with the device data sheet.
Note: The psychrometer is free from the disadvantage considered Augusta, in which both thermometers (dry and wet) are blown at a constant speed by an air flow created by a fan with a spring motor.
To dry materials, air heated in a heater or flue gases mixed with air are most often used as coolants and moisture carriers. Considering that the mixture of flue gases with atmospheric air in its thermophysical properties differs little from heated moist air, we will consider the most important characteristics of moist air.
Humid air is a mixture of dry air and water vapor. Humid air is characterized by the following basic parameters:
Absolute humidity determined by the amount of water vapor in kg,
Relative humidity , or the degree of air saturation () is the ratio of the mass of water vapor in 1 m 3 of humid air () to the maximum possible mass of water vapor in 1 m 3 of air (saturated vapor density) under the same conditions (t, P).
As the temperature increases, (saturated vapor density) increases faster than (vapor density), i.e. When heated, the relative humidity decreases.
Moisture content - this is the amount of water vapor (in kg) contained in moist air per 1 kg of absolutely dry air.
where and is the mass of water vapor and the mass of absolutely dry air in a given volume of moist air, kg.
According to the Mendeleev-Klaiperon equation,
Substituting these values into the formula for (x) moisture content, we get
Molecular weight of water vapor (18)
Molecular weight of dry air (29)
Ratio18/29=0.622
According to Dalton's law, the total pressure of the gas mixture (P) will be equal to the sum of the partial pressures of the components, i.e. for our case 
, given that, then 
,
where is the saturation pressure
Barometric pressure
Heat content or the enthalpy of moist air is expressed by the sum of the enthalpies of 1 kg of dry air () and water vapor () contained in it.
because heat capacity of air 
, and the heat capacity of water vapor 
. Water vapor is in the drying process in a superheated state mixed with air, then
Enthalpy of superheated steam at 0 0 C (=2493 kJ/kg)
Dry bulb temperature - denoted by the letter (or), this is the temperature that is around us.
Wet bulb temperature - the temperature of adiabatic saturation (i.e. without heat exchange with the environment) or this is the temperature of water evaporation from the free surface (denoted by ).
Drying potential - denoted by (g), this is the difference between the air temperature () and the wet thermometer temperature (), characterizes the ability of air to absorb moisture from the material.
Dew point temperature () is the saturation temperature of the air at constant moisture content.
Partial moisture pressure - this is the pressure that moisture vapor would create if these vapors occupied the volume occupied by the steam-air mixture.
The main instruments used to measure air parameters: (barometers, thermometers, psychrometers, hygrometers, recording instruments - barographs, thermographs).
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 forms of education
Saratov 2009
Goal of the work: deepening knowledge in the section of technical thermodynamics “Moist 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 the following should be learned:
1) basic concepts about moist air;
2) methodology for determining the parameters of humid air by
calculated dependencies;
3) methodology for determining the parameters of humid air by
I-d diagram.
1) determine the value of humid air parameters by
calculated dependencies;
2) determine the parameters of humid air using
I-d diagrams;
3) draw up a report on the laboratory work performed.
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 amount of water vapor.
A mixture of dry air and water vapor is called moist air. Humid air is widely used in drying, ventilation, air conditioning, etc.
A characteristic feature of the processes occurring in humid air is that the amount of water vapor contained in the air changes. Steam may partially condense and, conversely, water evaporates into the air.
A mixture consisting 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 pH, corresponding to the temperature of moist air (pp<рн). Температура пара выше температуры его насыщения при данном парциальном давлении.
A mixture consisting 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 the humid air. The steam temperature is equal to the condensation temperature at a given partial steam 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 suspended and fall out in the form of dew) is called supersaturated moist air. The partial pressure of water vapor is equal to the saturation pressure corresponding to the temperature of the moist air, which in this case is equal to the condensation temperature of the vapor contained in it. In this case, the temperature of the humid air is called the dew point temperature tR. If for some reason the partial pressure of water vapor is greater than the saturation pressure, then part of the vapor will condense in the form of dew.
The main indicators characterizing the state of humid air are moisture content d, relative humidity j, enthalpy I and density r.
Calculation of the parameters of moist air is carried out using the Mendeleev-Clapeyron equation for an ideal gas, to which moist air obeys with sufficient approximation. We 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 ditch- 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 rn, corresponding to the temperature of humid air.
The amount of water vapor in the 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– volume of gas mixture, m3;
RV, RP– gas constants of air and water vapor, equal
RV=287 J/(kg×K), RP=461 J/(kg×K);
T– temperature of humid air, K.
Considering that 
, and, substituting expressions (3) and (4) into formula (2), we finally obtain:
DIV_ADBLOCK64">
Relative humidity j is called the ratio of vapor density (that is, absolute humidity rP) to the maximum possible absolute humidity (density rPmax) at a given temperature and pressure of humid air:
Because rP And rPmax are determined at the same temperature of humid 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 by 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 water vapor:
I= iV+ 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, °С;
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 METHODS
EXPERIMENTAL RESULTS
Measure the temperature of the dry and wet thermometers. Determine the true value of the wet thermometer temperature using formula (13). Find the difference Dt = tc - tm ist and using a 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– volume of the room, m3;
R– humid air pressure, Pa.
Enter the calculation results and instrument readings into a table using the following form.
Protocol for recording readings of measuring instruments
and calculation results
Name of the value being 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 | ||||
Dry air partial pressure | ||||
Density of humid air | ||||
Absolute humidity | rP | |||
Gas constant of humid air | ||||
Enthalpy of moist air | ||||
Wet air mass |
Next, you should determine the main parameters of humid air from the measured tc And tm using an I-d diagram. The intersection point on the I-d diagram of the isotherms corresponding to the temperatures of the wet and dry thermometers characterizes the state of moist 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 absolute measurement error
The absolute error limit of the hygrometer in this laboratory work is ±6%. The absolute permissible error of psychrometer thermometers is ±0.2%. A barometer with an accuracy class of 1.0 is installed.
WORK REPORT
The report on the laboratory work performed must contain
following:
1) short description work;
2) a protocol for recording the readings of measuring instruments and
calculation results;
3) drawing with I-d diagram, where the wet condition is determined
air in this experiment.
CONTROL QUESTIONS
1. What is moist air called?
2. What is called saturated and unsaturated moist air?
3. Dalton's law as applied to moist air.
4. What is dew point temperature?
5. What is absolute humidity?
6. What is the moisture content of humid air?
7. Within what limits can moisture content vary?
8. What is called relative humidity?
9. In the I-d diagram, show the lines j=const, I=const; d=const, tс=const, tм=const.
10. What is the maximum possible vapor density at a given humid air temperature?
11. What determines the maximum possible partial pressure of water vapor in moist air and what is it equal to?
12. What parameters of moist air does the temperature of the wet thermometer depend on and how does it change when they change?
13. How can you determine the partial pressure of water vapor in a mixture 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 enthalpy of moist air?
LITERATURE
1. Lyashkov fundamentals of heating engineering /. M.: Higher School, 20 p.
2. Zubarev on technical thermodynamics / , . M.: Energy, 19 p.
DETERMINATION OF HUMID AIR PARAMETERS
Guidelines for performing laboratory work
in the courses “Thermal Engineering”, “Technical Thermodynamics and Thermal 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-bake l. Academic ed. l.
Circulation Order Free
Saratov State Technical University
Copy printer SSTU, 7
The state of moist air is determined by a set of parameters: air temperature t in, relative humidity in%, air speed V in m/s, concentration of harmful impurities C mg/m 3, moisture content d g/kg, heat content I kJ/kg.
Relative humidity in fractions or% shows the degree of air saturation with water vapor in relation to the state of complete saturation and is equal to the ratio of the pressure P p of water vapor in unsaturated humid air to the partial pressure P p. n. water vapor in saturated humid air at the same temperature and barometric pressure:
d= or d=623, g/kg, (1.2)
where B is barometric air pressure equal to the sum of the partial pressures of dry air P S.V. and water vapor R P.
The partial pressure of water vapor in a saturated state depends on temperature:
KJ/kg, (1.4)
where c B is the heat capacity of dry air, equal to 1.005;
c P - heat capacity of water vapor, equal to 1.8;
r - specific heat of vaporization, equal to 2500;
I \u003d 1.005t + (2500 + 1.8t) d * 10 -3, kJ / kg. (1.5)
I-d diagram humid air. Construction of the main processes of changing the state of air. Dew point and wet bulb thermometer. Angular coefficient and its connection with the flow of heat and moisture into the room
I-d diagram of humid air is the main tool for constructing processes for changing its parameters. The I-d diagram is based on several equations: heat content of moist air:
I = 1.005 * t + (2500 + 1.8 * t) * d/1000, kJ/kg (1.6)
in turn, water vapor pressure:
pressure of water vapor saturating the air:
Pa (Filney Formula), (1.9)
a - relative air humidity, %.
In turn, formula 1.7 includes barometric pressure P bar, which is different for different construction areas, therefore, to accurately construct processes, an I-d diagram is required for each area.
The I-d diagram (Fig. 1.1) has an oblique coordinate system to increase the working area related to moist air and lying above the line = 100%. The opening angle can be different (135 - 150º).
The I-d diagram links together 5 parameters of moist air: heat and moisture content, temperature, relative humidity and saturation water vapor pressure. Knowing two of them, you can determine all the rest by the position of the point.
The main characteristic processes on the I-d diagram are:
Air heating according to d = const (without increasing moisture content) Fig. 1.1, points 1-2. In real conditions, this is heating the air in the heater. Temperature and heat content increase. Relative air humidity decreases.
Air cooling according to d = const. Points 1-3 in Fig. 1.1 This process occurs in a surface air cooler. Temperature and heat content decrease. Relative air humidity increases. If we continue cooling, the process will reach the line = 100% (point 4) and, without crossing the line, will go along it, releasing moisture from the air (point 5) in the amount of (d 4 -d 5) g/kg. Air drying is based on this phenomenon. In real conditions, the process does not reach = 100%, and the final relative humidity depends on the initial value. According to Professor Kokorin O.Ya. for surface air coolers:
max = 88% with initial initial = 45%
max = 92% with initial 45%< нач 70%
max = 98% with initial initial > 70%.
On the I-d diagram, the cooling and drying process is indicated by a straight line connecting points 1 and 5.
However, the meeting with = 100% of the cooling line along d = const has its own name - this is the dew point. The dew point temperature is easily determined by the position of this point.
Isothermal process t = const (line 1-6 in Fig. 1.1). All parameters increase. Warmth, moisture content, and relative humidity increase. In real conditions, this is air humidification with steam. The small amount of sensible heat introduced by steam is usually not taken into account when constructing the process, since it is insignificant. However, such hydration is quite energy-intensive.
Adiabatic process I = const (line 1-7 in Fig. 1.1). Air temperature decreases, moisture content and relative humidity increase. The process is carried out by direct contact of air with water, passing either through an irrigated nozzle or through a nozzle chamber.
With an irrigated nozzle depth of 100 mm, you can obtain air with a relative humidity of = 45% with an initial 10%, a nozzle with a depth of 200 mm gives = 70%, and a 300 mm depth = 90% (according to data from VEZA cell humidification chambers). Passing through the nozzle chamber, the air is humidified to a value = 90 - 95%, but with significantly higher energy consumption for water spraying than in irrigated nozzles.
Continuing the line I = const to = 100%, we get the point (and temperature) of the wet thermometer, this is the equilibrium point when air comes into contact with water.
However, in devices where air comes into contact with water, especially in the adiabatic cycle, pathogenic flora may arise, and therefore such devices are prohibited for use in a number of medical and food industries.
In countries with hot and dry climates, devices based on adiabatic humidification are very common. So, for example, in Baghdad, at a daytime temperature in June - July of 46°C and a relative humidity of 10%, such a cooler allows you to reduce the temperature of the supply air to 23°C and, with 10-20 air exchanges in the room, achieve an internal temperature of 26°C and a relative humidity of 60-70%.
With the established methodology for constructing processes on the I-d diagram of moist air, the name of the reference points was given the following abbreviation:
H - outside air point;
B - point of internal air;
K - point after heating the air in the heater;
P - supply air point;
Y is the point of air removed from the room;
O - point of cooled air;
C is the point of mixture of air of two different parameters and masses;
TP - dew point;
TM is the point of the wet thermometer, which will accompany all further constructions.
When mixing air of two parameters, the mixture line will go along a straight line connecting these parameters, and the mixture point will lie at a distance inversely proportional to the masses of the air being mixed.
KJ/kg, (1.10)
G/kg. (1.11)
When excess heat and moisture are simultaneously released into the room, which usually happens when people are in the room, the air will be heated and humidified along a line called the angular coefficient (or process ray, or heat-humidity ratio) e:
KJ/kgN 2 O, (1.12)
where?Q n - total amount of total heat, kJ/h;
W - total amount of moisture, kg/h.
When?Q n = 0 e = 0.
When?W = 0 e > ? (Fig.1.2)
Thus, the I-d diagram in relation to internal air (or to another point) is divided into four quadrants:
I'm from? up to 0 - this is heating and humidification;
IIе from 0 to - ? - cooling and humidification;
IIIe from - ? up to 0 - cooling and drying;
IVе from 0 to? - heating and drying - not used in ventilation and air conditioning.
To accurately plot the process ray on the I-d diagram, you should take the value of e in kJ/gH 2 O, and put on the axis the moisture content d = 1, or 10 g, and on the axis the heat content in kJ/kg corresponding to e and connect the resulting point to point 0 I-d diagrams.
Processes that are not basic are called polytropic.
The isothermal process t = const is characterized by the value e = 2530 kJ/kg.
Fig.1.1
Fig.1.2 I-d diagram of humid air. Basic processes
