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PSYCHROMETRY
The capacity of air for moisture removal depends on its humidity and its temperature. The
study of a relationship between air and its associated water is called psychrometry.
Moist Air Properties
The drying medium used in drying cereal grains is moist air, which is a mixture of dry air and
water vapor. Dry air consists of a number of gases, mainly Oxygen and Nitrogen plus some
minor components such as Argon, Carbon dioxide, Neon, etc. Goff (1949), in determining the
thermodynamic properties of moist air, arbitrarily defined dry air as a gaseous mixture with a
molecular weight of 28.966 and a mole-fraction composition of 0.2095 Oxygen, 0.7809
Nitrogen, 0.0093 Argon and 0.0003 Carbon dioxide. Dry air may vary slightly from these
proportions at a given location; however, the Goff figures are sufficiently accurate for
engineering calculations.
In addition to the dry-air gases, moist air contains a varying amount of water vapor. Although
the weight fraction of water vapor in the air used for cereal grain drying is always less than
one-tenth, the presence of water vapor molecules has a profound effect on the drying process.
A number of terms are used to express the amount of water vapor in moist air. These and other
thermodynamic terms employed in describing moist air properties are defined in the following
section.
DEFINITION OF PSYCHROMETRIC TERMS
Three humidity terms are used in the grain-drying literature to characterize the amount of water
vapor held in the drying air:
Vapor pressure,
Relative humidity, and
Humidity ratio.
The temperatures of moist air may refer to the:
dry-bulb,
Page 1 of 20
dew-point or
Wet-bulb temperature.
Two additional moist-air properties frequently used in grain-drying calculations are:
Enthalpy and
Specific volume.
These nine moist-air thermodynamic properties are defined in the following paragraphs.
Vapor Pressure
The vapor pressure (Pv) is the partial pressure exerted by the water vapor molecules in moist
air. When air is fully saturated with water vapor, its vapor pressure is called the saturated vapor
pressure (Pvs).
Relative Humidity
The relative humidity () is the ratio of the mole fraction (or vapor pressure) of water vapor in
the air to the mole fraction (or vapor pressure) of the water vapor in saturated air at the same
temperature and atmospheric pressure. The relative humidity is expressed as a decimal or a
percentage. Relative humidity values between 0.0 and 100.0% are encountered in grain drying.
Humidity Ratio
The humidity ratio () is the weight of the water vapor contained in the moist air per unit
weight of dry air. Other terms used for humidity ratio are absolute humidity and specific
humidity.
Dry-bulb Temperature
The dry-bulb temperature (T) is the temperature of moist air indicated by an ordinary
thermometer. Whenever the term temperature is used in this book without a prefix, dry-bulb
temperature is implied.
Dew-point Temperature
The dew-point temperature (Tdp) is the temperature at which condensation occurs when the air
is cooled at constant humidity ratio and constant atmospheric pressure. Thus, the dew point
temperature can be considered as the saturation temperature corresponding to the humidity
ratio and vapor pressure of the moist air.
Page 2 of 20
Wet-bulb Temperature
A distinction should be made between the psychrometric and thermodynamic wet-bulb
temperatures. The psychrometric wet-bulb temperature (Twb) is the temperature of moist air
indicated by a thermometer whose bulb is covered with a wet wick. The airflow passing over
the wick should have a velocity of at least 5 m per sec.
The thermodynamic wet-bulb temperature (Twb*) is the temperature reached by moist air and
water if the air is adiabatically saturated by the evaporating water. The psychrometric and
thermodynamic wet-bulb temperatures of moist air are nearly equal.
Enthalpy
The enthalpy (h) of a dry air-water vapor mixture is the heat content of the moist air per unit
weight of dry air above a certain reference temperature. Since only differences in enthalpy are
of practical engineering interest, the choice of the reference temperature is inconsequential.
Specific Volume
The specific volume (v) of moist air is defined as the volume per unit weight of dry
air. The specific density of the moist air is equal to the reciprocal of its specific
volume
Page 3 of 20
PSYCHROMETRIC CHART
10 20 • t 30
Dry bulb temperature n °C
Construction
The thermodynamic properties of the dry air-water vapor mixture are frequently
needed in analyzing grain-drying problems. To alleviate the frequent necessity of
making the time-consuming calculations, special charts containing the values of the
most common thermodynamic properties of moist air have been prepared. These are
called psychrometric charts.
There are a number of psychrometric charts in use. The charts differ with respect
to the barometric pressure, the temperature range, the number of thermodynamic
properties included, and the choice of coordinates.
Page 4 of 20
Use of the Psychrometric Chart
Psychrometric charts give the following thermodynamic properties of moist air at one
atmosphere:
(1) Dry-bulb temperature,
(2) Wet-bulb temperature,
(3) Dew point (or saturation) temperature,
(4) Humidity ratio,
(5) Relative humidity,
(6) Specific volume, and
(7) Enthalpy.
If two of these properties are known, the state point of the air can, in general, be
determined on the chart and the other properties found by reading the values of the
appropriate lines which pass through the point.
Page 5 of 20
Sensible Heating and Cooling
Several processes relative to grain conditioning can be represented conveniently on the
psychrometric chart. During sensible heating and cooling of the air at constant
humidity ratio, heat is added to or withdrawn from the drying air in a heat exchanger
as in an indirect heater (for grain drying) or in an evaporator (for grain chilling).
The processes of sensible heating and cooling are represented on the psychrometric
chart by straight horizontal lines parallel to the abscissa (Fig. 2.3), and result in
changes in the dry and wet-bulb temperatures, the enthalpy, the specific volume and
the relative humidity of the moist air. No change occurs in the humidity ratio, dew
point temperature and vapor pressure of the moist air.
Page 6 of 20
Heating with Humidifying
In most heated-air grain-drying systems, energy is added to the air by direct
combustion of gas in the air. During this process not only heat but also a small
amount of water vapor is added to the air. The result of this heating and humidifying
process is that the enthalpy, the humidity ratio, the vapor pressure, the dry-bulb, wet-
bulb and dew point temperatures, and the specific volume of the air are increased. The
change in the relative humidity is determined by the relative amounts of energy and
water vapor added to the air. In grain-drying installations, the relative humidity of the
drying air decreases during the combustion of a fuel in the heater (Fig. 2.4).
Cooling with Dehumidifying
In the process of grain chilling, air is often cooled to below the dew point temperature
by passing it over an evaporator. Since the air is saturated with water vapor at the dew
point temperature, water condenses out of the air as soon as its temperature drops below
Tdp. The humidity ratio of the air will then be decreased, as will the dew point, wet-bulb
and dry-bulb temperatures and the enthalpy and specific volume. The cooling and
dehumidifying process is illustrated in Fig. 2.5.
Page 7 of 20
Drying
The drying of a column of grain can be considered an adiabatic process. This implies
that the heat required for evaporation of the grain moisture is supplied solely by the
drying air, without transfer of heat by conduction or radiation from the surroundings.
As the air passes through the wet grain mass, a large part of the sensible heat of the air
is transformed into latent heat as a result of the increasing amount of water held in the
air as vapor. During the adiabatic drying process there is a decrease in the dry-bulb
temperature, together with an increase in the humidity ratio and relative humidity, the
vapor pressure and the dew point temperature. The enthalpy and the wet-bulb
temperature remain practically constant during the adiabatic drying process. The
process of grain drying is illustrated in Fig. 2.6.
Page 8 of 20
Mixing of Two Airstreams.
In a number of continuous-flow grain dryers two streams of air with different mass
flow rates, temperatures, and humidity ratios are mixed. The condition of the resulting
mixture can be determined directly on the ASHRAE psychrometric charts.
Consider two air streams with dry mass flow rates of ml and m2, temperatures Tl
and T2 and humidity ratios Wi and W2. The mixture will have a dry mass flow rate of
m3, a temperature of T3 and a humidity ratio of W3. The mass and energy balances for
this process are:
ml + m2 = m3
m l W l + m2W2 = m3W3
m l h l + m2h2 = m3h3
Eliminating m3 yields:
M1(h3-h1) = m 2 (h 2 - h3)
m l (W 3 - W l ) = m 2 (W 2 - W3)
and thus:
Page 9 of 20
Re-arranging gives:
The condition of the mixture of the two air streams therefore lies on a straight line
joining (h 1 , W1) and (h2, W2) on the h-W psychrometric chart. The point ( h 3 , W3) can
be found algebraically or by applying the rule of the congruent right triangles directly
on the psychrometric chart. The mixing process is illustrated in Fig. 2.7.
EXAMPLE
If the wet-bulb temperature in a particular room is measured and found to be 20 C in air
whose dry-bulb temperature is 25 C (that is the wet-bulb depression is 5 °C) estimate the
relative humidity, the enthalpy and the specific volume of the air in the room.
On the humidity chart follow down the wet-bulb line for a temperature of 20°C until it Page 10 of 20
meets the dry-bulb temperature line for 25°C. Examining the location of this point of
intersection with reference to the lines of constant Relative humidity, it lies between 60%
and 70%RH and about 4/10 of the way between them but nearer to the 60% line.
Therefore the RH is estimated to be 64%. Similar examination of the enthalpy lines gives
an estimated enthalpy of 57 kJ / kg and from the volume lines a specific volume of 0.862m3 /kg
Once the properties of the air have been determined other calculations can easily
be made.
EXAMPLE
If the air in the above Example is then heated to a dry-bulb temperature of 40°C, calculate
the heat needed for a flow of 1000 m3 /hr of the hot air to be supplied to a dryer, and the
relative humidity of the heated air.
On heating, the air condition moves, at constant absolute humidity as no water vapour is
added or subtracted, to the condition at the higher (dry bulb) temperature of 40°C. At this
condition, reading from the chart, the enthalpy is 73kJkg-1, specific volume is 0.906
m3 /kg and RH.27 %.
Mass of 1000m3 is 1000/0.906 - 1104kg, - (73 - 57) = 16kJ/kg.
So rate of heating required
- 1104 x 16 Kj/hr
- (1104 x 16)/3600= 5kW.
If the air is used for drying, with the heat for evaporation being supplied by the hot air
passing over, a wet solid surface, the system behaves like the adiabatic saturation system. It is
adiabatic because no heat is obtained from any source external to the air and the wet solid, and
the latent heat of evaporation must be obtained by cooling the hot air. Looked at from the
viewpoint of the Solid, this is a drying process; from the viewpoint of the air it is
humidification.
Page 11 of 20
HOME WORK
Write short notes on:
a. Equilibrium moisture content
b. Constant rate drying
c. Falling Rate drying
(Use sketches and graphs to illustrate your answer)
Page 12 of 20
DRYING EQUIPMENT
In an industry so diversified and extensive as the food industry, it would be expected that a
great number of different types of dryer would be in use. This is the case and the total range of
equipment is much too wide to be described in any introductory course such as this. The
principles of drying may be applied to any type of dryer, but it should help the understanding
of these principles if a few common types of dryers are described.
The major problem in calculations of real dryers is that conditions change as the drying air and
the drying solids move along the dryer in a continuous dryer, or change with time in the batch
dryer. Such implications take them beyond the scope of the present course, but the principles
of mass and heat balances learned in FEB 423 are the basis and the analysis is not difficult
once the fundamental principles of drying are understood.
Tray Dryers
In tray dryers, the food is spread out, generally quite thinly, on trays in which the drying takes
place. Heating may be by an air current sweeping across the trays, by conduction from heated
trays or heated[shelves on which the trays lie, or by radiation from heated surf aces. Most tray
dryers are heated by air which also removes the vapours.
Tunnel Dryers
These may be regarded as developments of the tray dryer, in which the trays on trolleys move
where the heat is applied and the vapours removed . In most cases, air is used in tunnel drying
and the material can move through the dryer either parallel or countercurrent to the air flow.
Roller or Drum Dryers
In these the food is spread over the surface of a heated drum. The drum rotates, with the food
being applied to the drum at one part of the cycle. The food remains on the drum surface for
the greater part of the rotation, during which time the drying takes place, and is then scraped
off. Drum drying may be regarded as conduction drying:
Fluidized Bed Dryers
In a fluidized bed dryer, the food material is maintained suspended against gravity in an
upward-flowing air stream. There may also be a horizontal air flow to convey the food
through the dryer. Heat is transferred from the air to the food material, mostly by convection.
Spray Dryers
In a spray dryer, liquid or fine-solid material in a slurry is sprayed in the form of a fine
Page 13 of 20
dispersion into a current of heated air. Drying occurs very rapidly, so that this process is very
useful for materials which are damaged by exposure to heat for any appreciable length of time.
The dryer body is large so that the particles can settle, as they dry, without touching the walls
on which they might otherwise stick.
Pneumatic Dryers
In a pneumatic dryer, the solid food particles are conveyed rapidly in an air stream, the
velocity and turbulence of the stream maintaining the particles in suspension. Heated air
accomplishes the drying and often some form of classifying device is included in the
equipment. In the classifier, the dried material is separated, the dry material passes out as
product and the moist remainder is re-circulated for further drying.
Rotary Dryers
The foodstuff is contained in a horizontal inclined cylinder through which it travels, being
heated either by air flow through the cylinder, or by conduction of heat from the cylinder
walls. In some cases, the cylinder rotates and in others the cylinder is stationary and a paddle
or screw rotates within the cylinder conveying the material through.
Trough Dryers
The materials to be dried are contained in a trough-shaped conveyor belt, made from mesh,
and air is blown through the bed of material. The movement of the conveyor continually turns
over the material, exposing fresh surfaces to the hot air.
Bin Dryers
In bin dryers, the foodstuff is contained in a bin with a perforated bottom through which warm
air is blown vertically upwards, passing through the material and so drying it.
Belt Dryers
The food is spread as a thin layer on a horizontal mesh or solid belt and air passes through or
over the material. In most cases the belt is moving, though in some designs the belt is
stationary and the material is transported by scrapers.
Vacuum Dryers
Batch vacuum dryers are substantially the same as tray dryers, except that they operate under a
vacuum, and heat transfer is by conduction or by radiation. The trays are enclosed in a large
cabinet which is evacuated. The water vapour produced is generally condensed, so that the
vacuum pumps have only to deal with non-condensable gases. Another type consists of an
evacuated chamber containing a roller dryer.
Page 14 of 20
Freeze Dryers
The material is held on shelves or belts in a chamber which is under high vacuum. In most
cases, the food is frozen before being loaded into the dryer. Heat is transferred to the food by
conduction or radiation and the vapour is removed by vacuum pump and then condensed. The
pieces of food must be shaped so as to present the largest possible flat surface to the expanded
metal and the plates to obtain good heat transfer. A refrigerated condenser may be used to
condense the water vapour.
Various types of dryers are illustrated in Fig. 7.8.
Page 15 of 20
Page 16 of 20
MOISTURE LOSS IN FREEZERS AND CHILLERS
When a moist surface is cooled by an air flow, and if the air is unsaturated, water will
evaporate from the surface to the air. This contributes to the heat transfer, but a more
important effect is to decrease the weight of the foodstuff by the amount of water removed.
The loss in weight has serious economic consequences, since food is most often sold by
weight, and also in many foodstuffs the moisture loss may result in a less attractive surface
appearance. To give some idea of the quantities involved, meat on cooling from animal body
temperature to air temperature loses about 2 % of its weight, on freezing it may lose a further
1 % and thereafter if held in a freezer store it loses weight at a rate of aboutJX25 % per month.
After a time, this steady rate of loss in store falls off, but over the course of a year the total
store loss may easily be of the order of 2-2.5 %.
Drying
To minimize these weight losses, the humidity of the air in freezers, chillers and stores and the
rate of chilling and freezing, should be high. The design of the evaporator equipment can help
if a relatively large coil area has been provided for the freezing or cooling duty. The large area
means that the cooling demand can be accomplished with a small air-temperature drier. This
may be seen from the standard equation
q= UAT
For fixed q (determined by the cooling demand) and for fixed U (determined by the design of
the freezer) a large A will mean a small T, and vice versa. Since the air leaving the coils will
be nearly saturated with water vapour as it leaves, the larger the T the colder the air at this
point, and the dryer it becomes. The dryer it becomes (the lower the RH) the larger drying
capacity for absorbing water from the meat. So a low T decreases the drying effect. The
water then condenses from the air, freezes to ice on the coils must be removed from time to
time, by defrosting. Similarly for fixed U and A, a large q means a large T and therefore
better insulation leading to a lower q will decrease weight losses.
Page 17 of 20
SUMMARY
1. In drying:
(a) The latent heat of vaporization must be supplied,
(b) The moisture must be transported out from the food.
2. Rates of drying depend on:
(a) vapour pressure of water at the drying temperature,
(b) vapour pressure of water in the external environment,
(c) The equilibrium vapour pressure of water in the food,
(d) The moisture content of the food.
3. For most foods, drying proceeds initially at a constant rate given by:
dw/dθ = k'gA(Ys - Ya) = hcA(ta - ts)/ = q/
for air drying. After a time the rate of drying decreases as the moisture content of the food
reaches low values.
4. Air is saturated with water vapour when the partial pressure of water vapour in the air
equals the saturation pressure of water vapour at the same temperature.
5. Humidity of air is the ratio of the weight of water vapour to the weight of the dry air in the
same volume.
6. Relative humidity is the ratio of the actual to the saturation partial pressure of the water
vapour at the air temperature.
7. Water vapour/air humidity relationships are shown on the psychrometric chart.
Page 18 of 20
PROBLEMS
1. Cabbage containing 89% of moisture is to be dried in air at 65°C down to moisture content
on a dry basis of 5%. Calculate the heat energy required per tonne of/raw cabbage and per
tonne of dried cabbage, for the drying. Ignore the sensible heat.
2. The efficiency of a spray dryer is given by the ratio of the heat energy in the hot air supplied
to the dryer and actually used for drying, divided by the heat energy supplied to heat the air
from its original ambient temperature. Calculate the efficiency of a spray dryer with an inlet
air temperature of 150°C, an outlet temperature of 95°C, operating under an ambient air
temperature of 15°C Suggest how the efficiency of this dryer might be raised.
3. Calculate the humidity of air at a temperature of 65°C and in which the RH is 42 % and
check from a psychrometric chart.
4. Water at 36°C is to be cooled in an evaporative cooler by air which is at a temperature of
18°C and in which the-RH is measured to be 43 %. Calculate the minimum temperature to
which the air could be cooled, and if the air is cooled to 5°C above this temperature, what is
the actual cooling effected. Check your results on a psychrometric chart.
5. In a chiller store for fruit, which is to be maintained at 5°C, it is important to maintain a
daily record of the relative humidity. A wet- and dry-bulb thermometer is available so prepare
a chart giving the relative humidity for the store in terms of the wet-bulb depression.
6. A steady stream of 1300 m3 h] of room air at 16°C and 65 % RH is to be heated to 150°C
to be used for drying. Calculate the heat input required to accomplish this. If the air leaves the
dryer at 92°C and at 98 % RH calculate the quantity of water removed per hour by the dryer.
7. In a particular situation, the heat-transfer coefficient from a food material to air has been
measured and found to be 25 Jm-2 s-1 °C-1. If this material is to be dried in air at 90°C and 15 %
RH, estimate the maximum rate of water removal.
8. Considering apples to be spheres of diameter 0.07 m and of density 960 kg m -3, estimate
Page 19 of 20
the rate of drying of apples, per cent per week, if they are in air at 12°C and 65 % RH flowing
over the apples at 0.5ms-1.
Page 20 of 20