Psychrometry of Air-Conditioning Processes

 

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Psychrometry, the study of the thermodynamic properties of moist air, is essential for understanding and designing air-conditioning systems. This section focuses on the adiabatic mixing of air streams and how these processes affect the properties of moist air.

1.0 Mixing Processes

In air-conditioning applications, air streams of different temperatures and moisture contents are often mixed. This section describes the adiabatic mixing of two air streams at constant pressure.

Adiabatic Mixing of Air Streams

Let’s denote:

• Subscripts 1 and 2 for the two air streams.
• Subscript 3 for the resultant mixture.
• $m_a$ for the mass of dry air in each stream.

Moisture Balance Equation:
The specific humidity $\omega$ of the mixture can be determined using the moisture balance:

$$m_{a3}{\omega }_3=m_{a1}{\omega }_1+m_{a2}{\omega }_2$$

From this, the specific humidity of the mixture is given by:

$${\omega }_3=\frac{m_{a1}{\omega }_1+m_{a2}{\omega }_2}{m_{a3}}$$

Where the mass of dry air in the mixture is:

$$m_{a3}=m_{a1}+m_{a2}$$

Energy Balance Equation:
The enthalpy of the mixture can be found using the energy balance:

$$h_3=\frac{m_{a1}{h}_1+m_{a2}{h}_2}{m_{a3}}$$

Moreover, the temperature can be approximated as:

$$t_3\approx \frac{m_{a1}{t}_1+m_{a2}{t}_2}{m_{a3}}$$

The approximation assumes that the humid specific heat $C_p$ remains constant across the three streams.

Graphical Representation on the Psychrometric Chart

In psychrometry, processes involving moist air can be plotted on a psychrometric chart, which provides a graphical representation of the relationships between temperature, humidity, and enthalpy.

1. On the $\omega -h$ Coordinate System:

   • The state point for the mixture (point 3) lies on the straight line connecting the two individual states (points 1 and 2). This is a result of the defined relationships for specific humidity and enthalpy.

2. On the $\omega -t$ Coordinate System:

   • The position of the mixture state point (point 3) approximately divides the line joining states 1 and 2 based on the inverse ratio of the masses of the dry air streams $m_{a1}$ and $m_{a2}$.

Mixing Process on Psychrometric Chart

The psychrometric chart offers clear visual insights into the changes occurring during the mixing processes:

• State Points: Each stream of moist air (1 and 2) and the resultant mixture (3) can be represented as points on the chart, each defined by their specific enthalpy and specific humidity.
• Lines of Constant Enthalpy: The process of mixing occurs along lines of constant enthalpy if the system is well mixed and adiabatic.

The psychrometry of air-conditioning processes, particularly concerning mixing, is vital for designing effective systems. By understanding the relationships between specific humidity, enthalpy, and temperature, engineers can optimize air-conditioning design, enhance energy efficiency, and create comfortable indoor environments. This framework aids in predicting how specific mixtures of air will behave under various conditions, providing the foundation for effective climate control solutions.

SAMPLE PROBLEM:

 A 30 m3/min of stream moist air at 15 oC DBT and 13 0c WBT are mixed with 12 m3/min of a second stream  at 25 oC DBT and 18 oC WBT. Barometric pressure is one standard atmosphere (1.013 bar/14.7psi). Determine the following:

a. The dry air mass flow rates of the first and second air streams.

b. The total dry air mass flow rate, specific humidity, the enthalpy, dry bulb, and wet bulb temperatures of the resulting mixture.

Basic Processes in Conditioning of Air

In the context of air-conditioning, various thermodynamic processes are utilized to manipulate the state of moist air effectively. These processes can be classified into four basic individual processes and four combinations of processes that alter the properties such as temperature and humidity of the air. Understanding these processes is fundamental for HVAC engineering and environmental control.

Four Basic Processes

Sensible Heating (Process O-A)
This process involves raising the air's dry bulb temperature (DBT) while maintaining a constant moisture content (specific humidity). It is represented on the psychrometric chart as a horizontal line moving from left to right.

SAMPLE PROBLEM:

A   14 m3/min. of air  at  20 oC and 80 percent relative humidity  is to raise its temperature to   35 oC . Determine the following:

Enthalpy of the air/kg of d.a. , h1 =  

Enthalpy of the air/kg of d.a., h2 = 

Specific of volume air/kg of d. a., v1=

Mass flow rate of dry air , kg/min, ma =

Relative humidity, Ø = %

The heat required or heat  transfer or sensible heat, Q

From the psychrometric chart at  tdb1 = 20 oC and  Ø 1 =80 %

                                                      *** tdb1 =  dry bulb temperature (DBT) 

                   

Sensible Cooling (Process O-B)
In this process, the DBT of the air is decreased while the moisture content remains unchanged. It is depicted on the psychrometric chart as a horizontal line moving from right to left.

SAMPLE PROBLEM:

Determine the quantity of heat removed from  14 m3/min of air when cooled from 37 oC dry bulb  and 21 0C wet bulb temperatures to 15 oC. Determine the following:

 a)  The initial relative humidity

  b) Mass flow rate of dry air, ma1 

  c) The final relative humidity and h2 

  d) Heat removed from the 14m3/min of air

3.Chemical Dehumidifying

-Air can be dehumidified by passing it over chemicals that have an affinity for moisture. 

-Usually in so doing the moisture is condensed and gives up its latent heat, raising the dry bulb temperature of the air.

-The air leaves drier and warmer. 

-The wet bulb temperature may increase or decrease .

Units employing such chemical are used in some comfort air conditioning installations but mainly for industrial air conditioning.

Since the leaving-air temperature is usually higher than wanted, it is necessary to add a sensible cooling process to get the desired final air conditioning. 

SAMPLE PROBLEM:

Air at 24 0C dry bulb and 15 0C wet bulb temperatures enters a dehumidifier and leaves at 41 0C dry bulb and 19 0C wet bulb temperatures. How much moisture has been removed per kilogram of dry air.

Four Combination Processes

1. Heating and Humidifying (Process O-E)
   This process occurs when air is heated while moisture is added, such as when air passes over warm water. The result is an increase in both temperature and specific humidity.

   

   
   

SAMPLE PROBLEM:

 A 28 m3/min  of air at 24 0C and 40 per cent relative humidity is  to raise it to  35 0C dry bulb and 27 0C  wet bulb temperatures. Determine the following:

a. Mass flow rate

b. Heat added to a 28 m3/min of air .

c. Moisture added to a 28 m3/min of air.

1. Cooling and Dehumidifying (Process O-F)
   In this process, the air is cooled while simultaneously reducing its moisture content, typically by passing it over cold surfaces. This results in a decrease in both temperature and specific humidity.

   

   
   

SAMPLE PROBLEM:

A 28 m3 per minute of air from 35 0C dry bulb and  26 0C wet bulb temperatures to cool at 21 0C and 50 percent relative humidity. Determine the following:

a. Mass flow rate

b. Heat must be removed.

c. Moisture must be removed. 

1. Cooling and Humidification (Process O-G)
   Here, air is cooled while its humidity is increased, often through the introduction of moisture in the form of a spray. This typically results in lower DBT and increased specific humidity.

   
   

SAMPLE PROBLEM:

Air at 33 0C dry bulb and 19 0C wet bulb temperatures is cooled and humidified by passing it through an air washer in which the water is continuously recirculated. The air leaves the air washer at 23 0C dry bulb temperature. Determine the moisture added per kg of dry air. What is the efficiency of the washer? 

Overview of Psychrometric Processes

• Sensible Heating and Cooling:
  Involve only changes in the dry bulb temperature with no change in moisture content.

• Humidifying and Dehumidifying:
  Cause changes in humidity ratio while keeping the DBT constant.

• The last four combination processes involve simultaneous changes in temperature and humidity ratio.

Practical Applications

Chemical Dehumidification:
Involves passing air over desiccant materials that absorb moisture, leading to a drier but potentially warmer condition of the air. This process is prevalent in industrial settings.

Cooling Coils and Spray Chambers:
Both are utilized for cooling and dehumidifying air. Cooling coils lower the temperature of the air by conducting heat away, while spray chambers add moisture and reduce the temperature through evaporation.

Methods of Air Dehumidification: Understanding Humidity Control

Humidity control is crucial for maintaining comfort and protecting materials in various environments. The removal of moisture from the air can be achieved through several methods:

1. Cooling and Condensation of Vapor

In cooling systems, humidity is reduced by cooling the air below the dew point. This causes a portion of the moisture in the air to condense and drain out. The process can vary based on the efficiency of the cooling system and the amount of moisture present in the air.

2. Adsorption of Water Vapor

Adsorption involves the use of materials like silica gel or activated alumina to reduce humidity.

How Adsorption Works:

• It is a physical process where moisture is condensed and held on the surface of the adsorbent material.
• Importantly, there is no change to the physical or chemical structure of the material, meaning it can be reactivated for continued use.

Reactivation Process:

• Temperature for Reactivation: 160-170 °C
• Heat Required for Reactivation: 4800 kJ/kg of water removed

Silica Gel

Silica gel (SiO2) is a hard, crystalline substance that is highly porous.

• Porosity: 50-70% by volume
• Water Absorption: Up to 40% of its mass
• Bulk Density: 480-720 kg/m³
• Specific Heat: 1.13 kJ/kg·K

Activated Alumina

Activated alumina is primarily composed of aluminum oxide (Al2O3) and is also very porous.

• Porosity: 50-70% by volume
• Water Absorption: Up to 60% of its mass
• Bulk Density: 800-870 kg/m³
• Specific Heat: 1.0 kJ/kg·K

3. Absorption of Water Vapor

Absorption systems utilize materials like calcium chloride solution to reduce humidity. Unlike adsorption, absorption involves a change in the physical or chemical structure of the absorbent material, making it generally more difficult to reactivate.

Cooling Load and Air Quantities

To adequately handle the cooling load, the quantity of air circulated must be sufficient. As the air warms up to room temperature, the following considerations come into play:

• The lower the supply temperature, the less air must be circulated.
• Factors like system design, draft prevention, cold regions, ceiling height, and throw requirements influence minimum supply temperature.

Understanding Sensible and Latent Heat Loads

Sensible Heat Load

Every building conditioned with HVAC systems experiences a sensible heat load, which accounts for heat gain or loss due to transmission. The design cooling load is defined as the heat energy to be removed from a house to maintain the indoor design temperature under the worst-case outdoor conditions.

Sensible Heat Calculation

The sensible heat load can be represented by the formula:

$$Q_s=m\cdot c_p\cdot (t_2-t_1)$$

Where:

• $Q_s$ = sensible heat load (kJ/s or kW)
• $m$ = mass flow rate of supply air (kg/s)
• $c_p$ = specific heat of humid supply air (approximately 1.0062 kJ/kg·°C)
• $t_2$ = desired inside space temperature (°C)
• $t_1$ = supply air temperature entering space (°C)

SAMPLE PROBLEM:

An auditorium is to be maintained at a temperature of 25 0C dry bulb temperature and 19 0C wet bulb temperatures . The sensible heat load is 88 kW and 58 kg per hour of moisture must be removed. Air is supplied to the auditorium at 18 0C. Determine the following: 

Understanding Latent Heat Load in Air Conditioning

Latent heat load is a critical concept in air conditioning, particularly in managing humidity levels within a building. All pure substances can change their state; solids can become liquids, and liquids can become gases without affecting the temperature of the substance. This principle is essential when considering how moisture affects indoor air quality and comfort.

The Role of Latent Heat Load

During the cooling cycle, condensation occurs within the air conditioning unit due to the removal of latent heat from the air. The latent capacity refers to the ability to remove moisture from the air.

Moisture Gain and Loss

• Moisture Gain: If a building gains moisture, it requires the condensation of moisture for dehumidification, resulting in a cooling load.
• Moisture Loss: Conversely, if a building loses moisture, it necessitates the evaporation of water for humidification, leading to a heating load.

Latent Heat Load Calculation

The moisture picked up by the air conditioning system can be calculated using the formula:

$$\text{Moisture picked up}=({\omega }_2-{\omega }_1)\text{kg/kg dry air}$$

Where:

• ${\omega }_2$ = humidity ratio of inside air (kg/kg)
• ${\omega }_1$ = humidity ratio of supply air (kg/kg)

The latent heat of water vapor in air conditioning is approximately 2500 kJ/kg, or the latent heat of vaporization of water at 0 °C is 2501 kJ/kg.

Latent Heat Load Formula

The latent heat load can be expressed as:

$$Q_L=m\cdot ({\omega }_2-{\omega }_1)$$

Where:

• $Q_L$ = latent heat load (kW)
• $m$ = mass flow rate of air (kg/s)
• $2500\text{kJ/kg}$ is the latent heat of vaporization.

Thus, the equation becomes:

$$Q_L=2500\cdot m\cdot ({\omega }_2-{\omega }_1)\text{kJ/s or kW}$$

Total Heat Load

The total heat load in an air conditioning system can be calculated by combining both sensible and latent heat loads:

$$Q_T=Q_s+Q_L$$

Where:

• $Q_T$ = total heat load (kW)
• $h_2$ = enthalpy of inside air (kJ)
• $h_1$ = enthalpy of supply air (kJ/kg)

The total heat load can also be expressed as:

$$Q_T=m\cdot (h_2-h_1)$$

Sensible Heat Ratio (SHR)

The sensible heat ratio (SHR) is defined as the ratio of the sensible heat load to the total heat load:

$$\text{SHR}=\frac{Q_s}{Q_s+Q_L}=\frac{Q_s}{Q_T}$$

Sensible Heat Factor (SHF)

The sensible heat factor (SHF) is the ratio of the total sensible heating load to the total heating load of the air conditioning apparatus. SHF is crucial in the design process of air conditioning systems. If the SHF is known for a particular cooling coil and the sensible load is provided, the total heat load capacity of the coil can be determined.

In summary, understanding latent heat load and its implications on air conditioning design is essential for effective humidity control and maintaining indoor comfort.

Various Methods of Handling the Air Supplied to Conditioned Space

Effective air handling is crucial for maintaining indoor air quality and comfort in conditioned spaces. Here are several methods for managing the air supplied to these environments:

A) All Outside Air Supplied and No Recirculation Air

Using all outside air with no recirculation can be economical under certain conditions. However, this method is most effective when the outside temperature and humidity levels are significantly different from the indoor conditions.

Considerations:

• Cost-Effectiveness: This method can be cost-effective when outside conditions are favorable.
• Odor Control: Recirculation is impractical in spaces where objectionable odors are present, making the use of all outside air necessary.

SAMPLE PROBLEM:

In a space, the sensible heat load is 13.5 kW and the latent heat load is 3.4 kW. The space is to be maintained at 25 oC dry bulb and 18 oC wet bulb temperatures. All outside air is supplied with reheater to satisfy the space conditions. The conditioned air leaves the supply fan at 17 0C. Determine a) the refrigeration load, b) the capacity of the supply fan, and c) the heat supplied in the reheater.

B) Recirculated and Outside Air Supplied

This method combines both recirculated air and outside air. It allows for better control of indoor air quality while reducing energy costs associated with conditioning entirely outside air.

Benefits:

• Energy Efficiency: By mixing recirculated air with outside air, the system can maintain desired indoor conditions more efficiently.
• Improved Air Quality: This method helps in diluting indoor pollutants while still utilizing some outside air for freshness.

SAMPLE PROBLEM:

An air conditioned theater is to be maintained at 26.7 0C dry bulb temperature and 50% relative humidity. The calculated total sensible load in the theater is 126,240kcal/h and latent heat load is 82,920 kcal/h. The air mixture (recirculated and outside air) at 28.9 dry bulb and 22 0C wet bulb temperatures is cooled  to 17.22 0C and 15 0C wet bulb temperatures by chilled water cooling coils and  delivered as supply air to the theater. Determine the following:

Enthalpy of air at point 1, kj/kg

Enthalpy at point 2, kJ/kg

Enthalpy at point 3, kJ/kg

Total heat load, QT in Kcal/hr and kJ/hr

Total mass flow rate of air, m in kg/hr, use QT = m (h3 –h2)

Refrigerating load , TR= m(h1-h2)

Room sensible heat factor (RSHF)

C) Recirculated Air with Internal-Bypass System

An internal-bypass system allows for the recirculation of air within the conditioned space while bypassing certain areas or components of the air handling system. This method can enhance comfort and efficiency.

Advantages:

• Enhanced Comfort: By controlling the flow of air, this system can help maintain consistent temperatures and humidity levels throughout the space.
• Flexibility: The internal-bypass system provides flexibility in managing air distribution, allowing for adjustments based on occupancy and usage patterns.

SAMPLE PROBLEM:

The air-handling unit of an air-conditioning plant supplies a total load of 4500 cmm of dry Air which comprises by weight 20 percent fresh air at 40 oC and 27 oC WBT, and 80 per cent recirculated air at 25 oC DBT and 50 per cent RH. The air leaves the cooling coil at 13 oC saturated state. Calculate the  ω1, h1, and t1.

Choosing the appropriate method for handling air in conditioned spaces depends on various factors, including energy efficiency, indoor air quality, and specific environmental conditions. Understanding these methods allows for better design and operation of HVAC systems, ensuring optimal comfort and health for occupants.

READ MORE: AREA 3 (AB STRUCTURES & ENVIRONMENT ENGINEERING & BIOPROCESS ENGINEERING &  ALLIED SUBJECTS)