chapter 2 revised

Chapter 2: Psychrometrics7 TYPICAL AIR-CONDITIONING PROCESSES 7.1 Moist Air Sensible Heating or Cooling Example 2: Moist air, saturated at 2°C, enters a heating coil at a rate of 10 m3/

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Anh văn Chuyên ngành Nhiệt

English for thermal engineering

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TÀI LIỆU THAM KHẢO

(1) 2017 ASHRAE Handbook—Fundamentals (SI)

(2) Fundamentals of thermal-fluid science, Y A Çengel.

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Chapter 2: Psychrometrics

(1) COMPOSITION OF DRY AND MOIST AIR

(2) PERFECT GAS RELATIONSHIPS FOR DRY AND MOIST AIR (3) HUMIDITY PARAMETERS

(4) THERMODYNAMIC WET-BULB AND DEW-POINT TEMP (5) OTHER PROPERTIES OF THE MOIST AIR

(6) PSYCHROMETRIC CHARTS

(7) TYPICAL AIR-CONDITIONING PROCESSES

Psychrometry is the study of the thermodynamics of

gas-vapor mixtures.

CONTENTS

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 Atmospheric air contains many gaseous (ˈɡeɪ.si.əs) components

( kəmˈpəʊ.nənt) as well as water vapor and miscellaneous

contaminants (e.g., smoke, pollen, and gaseous pollutants not normally

present in free air far from pollution sources)

 Dry air is atmospheric air with all water vapor and contaminants;

removed

 Moist air is a binary (two-component) mixture of dry air and water vapor

Harrison (1965) lists the approximate percentage composition of dry air by volume as:

nitrogen, 78.084; oxygen, 20.9476; argon, 0.934; neon, 0.001818; helium, 0.000524;

methane, 0.00015; sulfur dioxide, 0 to 0.0001; hydrogen, 0.00005; and minor components

(1) COMPOSITION OF DRY AND MOIST AIR

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When moist air is considered a mixture of independent perfect gases (i.e., dry air and water vapor), each is assumed to obey the perfect gas equation of state as follows:

(2) PERFECT GAS RELATIONSHIPS FOR DRY AND

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Humidity ratio, w

The humidity ratio of moist air w is the ratio of the mass of water vapor

m w to the mass of dry air m da contained in the mixture of the moist air,

in (kg/kgda)

The saturation humidity ratio, ws

, kg/kgda

, kg/kgdaChapter 2: Psychrometrics

𝑝𝑤𝑠 −represents the saturation pressure of water vapor in the absence of air

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 Absolute humidity, 𝝆𝒘

%

 Relative humidity, 𝛗

Relative humidity is the amount of moisture in the air compared to

what the air can “hold” at that temperature

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 Dry bulb temperature, 𝒕𝑫𝑩

(4) THERMODYNAMIC WET-BULB AND DEW-POINT

TEMPERATURE

Dry-bulb temperature can be measured

using a normal thermometer freely exposed

to the air but shielded from radiation and

moisture.

 Wet bulb temperature, 𝒕𝑾𝑩

Thermometer’s bulb is covered by a wick that has

been thoroughly wetted with water When the wet

bulb is placed in an airstream, water evaporates

from the wick, eventually reaching an equilibrium

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TEMPERATURE

- The wick should be saturated

- The air velocity around the wick should be from 5-10 m/s

- Unsaturated air: 𝑡𝐷𝐵>𝑡𝑊𝐵

- As 𝜑 = 100%  𝑡𝐷𝐵 = 𝑡𝑊𝐵 = 𝑡𝐷𝑃

- At the difference between 𝑡𝐷𝐵 and

𝑡𝑊𝐵 depends on the relative humidity 

A sling psychrometer

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 Dew point temperature, 𝒕𝑫𝑷

TEMPERATURE

The dew-point temperature 𝒕𝑫𝑷 is defined as the temperature at

which condensation begins when the air is cooled at constant

pressure.

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 Dew point temperature, 𝒕𝑫𝑷

𝐶14 = 6.54 𝐶15 = 14.526 𝐶16 = 0.7389 𝐶17 = 0.09486 𝐶18 = 0.4569

𝛼 = 𝑙𝑛𝑝𝑤

𝑝𝑤 − partial pressure of water vapor, kPa

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 Specific volume of the moist air, 𝝂

p – Total pressure, kPa

 Density of a moist air, 𝝆

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 The specific enthalpy of moist air, h

ℎ = 1.006𝑡 + 𝑤 2501 + 1.86𝑡 , kJ/kgda

(5) OTHER PROPERTIES OF THE MOIST AIR

𝑡 – Dry bulb temperature,  C

w – Humidity ratio, kgw/kgda

where

hda is the specific enthalpy for dry air in kJ/kgda

hg is the specific enthalpy for saturated water vapor in kJ/kgw

As an approximation,

ℎ𝑑𝑎 ⋍ 1.006𝑡 ℎ𝑔 ≃ 2501 + 1.86𝑡

ℎ = ℎ𝑑𝑎 + 𝑤ℎ𝑔 , kJ/kgda

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A psychrometric chart graphically represents the thermodynamic

properties of moist air

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7.1 Moist Air Sensible Heating or Cooling

Example 2: Moist air, saturated at 2°C, enters a heating coil at a

rate of 10 m3/s Air leaves the coil at 40°C Find the required rate of heat addition

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7.1 Moist Air Sensible Heating or Cooling

Example 2:

𝑞12 = ሶ𝑚𝑑𝑎 ℎ2 − ℎ1

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7.2 Moist Air Cooling and Dehumidification

For the system in the figure, the steady-flow energy and

material balance equations are:

𝑚𝑑𝑎ℎ1 = ሶ𝑚𝑑𝑎ℎ2 + 𝑞12 + ሶ𝑚𝑤ℎ𝑤2

𝑚𝑑𝑎𝑤1 = ሶ𝑚𝑑𝑎𝑤2 + ሶ𝑚𝑤thus,

𝑚𝑤 = ሶ𝑚𝑑𝑎 𝑤1 − 𝑤2

𝑞12 = ሶ𝑚𝑑𝑎 ℎ1 − ℎ2 − 𝑤1 − 𝑤2 ℎ𝑤2

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7.2 Moist Air Cooling and Dehumidification

Example 3:

Moist air at 30°C dry-bulb

temperature and 50% rh enters a

cooling coil at 5 m3/s and is

processed to a final saturation

condition at 10°C

Find the kW of refrigeration required

Solution:

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7.3 Adiabatic Mixing of Two Moist Airstreams

Adiabatic mixing is governed by three equations:

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Example 3:

A stream of 2 m3/s of outdoor air at 4°C dry-bulb temperature

and 2°C thermodynamic wet-bulb temperature is adiabatically

mixed with 6.25 m3/s of recirculated air at 25°C dry-bulb

temperature and 50% rh

Find the dry-bulb temperature and thermodynamic wet-bulb

temperature of the resulting mixture

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Example 3:

𝑙𝑖𝑛𝑒 3 − 2𝑙𝑖𝑛𝑒 1 − 3 =

𝑚𝑑𝑎1

𝑚𝑑𝑎3or

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7.4 Adiabatic Mixing of Water Injected into Moist Air

Steam or liquid water can be injected into a moist airstream to raise its humidity, as shown in below figure If mixing is adiabatic, the

following equations apply:

𝑚𝑑𝑎ℎ1 + ሶ𝑚𝑤ℎ𝑤 = ሶ𝑚𝑑𝑎ℎ2

𝑚𝑑𝑎𝑤1 + ሶ𝑚𝑤 = ሶ𝑚𝑑𝑎𝑤2Therefore

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7.4 Adiabatic Mixing of Water Injected into Moist Air

Example 5:

Moist air at 20°C dry-bulb and 8°C thermodynamic wet-bulb

temperature is to be processed to a final dew-point

temperature of 13°C by adiabatic injection of saturated steam

at 110°C The rate of dry airflow is 2 kgda/s Find the final

dry-bulb temperature of the moist air and the rate of steam flow

ℎ2 − ℎ1

𝑤2 − 𝑤1 =

∆ℎ

∆𝑤 = ℎ𝑔 = 2.691, kJ/gw

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7.5 Space Heat Absorption and Moist Air Moisture Gains

Air conditioning required for a

space is usually determined by

(1) the quantity of moist air to be

supplied, and (2) the supply air

condition necessary to remove

given amounts of energy and

water from the space at the

exhaust condition specified

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𝑚𝑑𝑎ℎ1 + 𝑞𝑠 + ෍ ሶ𝑚𝑤ℎ𝑤 = ሶ𝑚𝑑𝑎ℎ2

𝑚𝑑𝑎𝑤1 + ෍ ሶ𝑚𝑤 = ሶ𝑚𝑑𝑎𝑤2or

The quantity qs denotes the heat gain in the space, or sensible

heat gain

The quantity of σ𝑚ሶ 𝑤 is called as Moisture gain

Assuming steady-state conditions, governing equations are

𝑞𝑠 + ෍ ሶ𝑚𝑤ℎ𝑤 = ℎ2 − ℎ1 𝑚ሶ 𝑑𝑎

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Example 6:

Moist air is withdrawn from a room at 25°C dry-bulb temperature

and 19°C thermodynamic wet-bulb temperature The sensible

rate of heat gain for the space is 9 kW A rate of moisture gain of

0.0015 kgw/s occurs from the space occupants This moisture is

assumed as saturated water vapor at 30°C Moist air is

introduced into the room at a dry-bulb temperature of 15°C Find

the required thermodynamic wet-bulb temperature and volume

flow rate of the supply air

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through state 2 The intersection of this line with the 15°C

dry-bulb temperature line is state 1 Thus, 𝑡𝑊𝐵= 14.0°C

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𝑉1 = 𝑣1 × ሶ𝑚𝑑𝑎 = 0.829 × 0.873 = 0.724 m3/s

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Psychrometric charts online

1 http://daytonashrae.org/psychrometrics

/psychrometrics_si.html

2 http://www.flycarpet.net/en/psyonline

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1 http://daytonashrae.org/psychrometrics

/psychrometrics_si.html

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2 http://www.flycarpet.net/en/psyonline

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1 The air in a room is at 1 atm, 32C, and 60 percent relative humidity Use the psychrometric chart or available software Determine

(a) the specific humidity;

(b) the enthalpy (in kJ/kgda);

(c) the wet-bulb temperature;

(d ) the dew-point temperature;

(e) the specific volume of the air (in m3/kgda)

Homework

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2 Air enters a 30-cm-diameter cooling section at 1 atm, 35C, and

60 percent relative humidity at 120 m/min The air is cooled by

passing it over a cooling coil through which cold water flows The

water experiences a temperature rise of 8C The air leaves the

cooling section saturated at 20C Determine (a) the rate of heat

transfer, (b) the mass flow rate of the water, and (c) the exit

velocity of the airstream

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3 Two airstreams are mixed steadily and adiabatically The first

stream enters at 32C and 40 percent relative humidity at a rate of

20 m3/min, while the second stream enters at 12C and 90 percent relative humidity at a rate of 25 m3/min Assuming that the mixing process occurs at a pressure of 1 atm, determine the specific

humidity, the relative humidity, the drybulb temperature, and the

volume flow rate of the mixture

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