Psychrometric Processes

When discussing psychrometric processes, it is crucial to understand the fundamental principles that govern the behavior of air-water vapor mixtures. Psychrometrics involves the study of the thermodynamic properties of moist air, which are essential for various applications such as HVAC (Heating, Ventilation, and Air Conditioning) systems, meteorology, and industrial processes.

Key Concepts in Psychrometrics

1. Dry Bulb Temperature (DBT): This is the temperature of air measured by a standard thermometer. It does not account for moisture content and is a primary indicator of thermal conditions.

2. Wet Bulb Temperature (WBT): This measurement is taken using a thermometer covered with a water-soaked cloth over which air flows. It reflects the cooling effect of evaporation and is always lower than or equal to the DBT.

3. Relative Humidity (RH): This is the ratio of the current absolute humidity to the highest possible absolute humidity (which depends on the current air temperature). Expressed as a percentage, RH indicates how saturated the air is with moisture.

4. Dew Point Temperature: The temperature at which air becomes fully saturated with moisture and water begins to condense. This is critical for predicting weather phenomena and managing indoor air quality.

Psychrometric Chart

A view of psychrometric chart is shown before. It shows the relationship between dry-bulb temperature (the temperature measured by a regular thermometer), wet-bulb temperature (the temperature measured by a thermometer with a wetted bulb), relative humidity (the amount of moisture in the air compared to the maximum amount it can hold at that temperature), and dew point temperature (the temperature at which the air becomes saturated and condensation begins).

The curved lines represent constant relative humidity, while the diagonal lines represent constant wet-bulb temperature.

The following equation represents the heat transfer in a thermodynamic process involving a fluid. Here, 𝑄_𝐶​ is the heat added or removed, 𝑚𝑎ma​ is the mass flow rate of the fluid, ℎ₁​ and ℎ₂​ are the specific enthalpies at the initial and final states, respectively, and 𝐶_𝑝,𝑚​ is the specific heat capacity at constant pressure. The term (𝑇₂−𝑇₁) denotes the temperature change of the fluid from the initial state 𝑇₁​ to the final state 𝑇_2​. This equation essentially states that the heat transfer 𝑄_𝐶​ is proportional to the mass flow rate and the change in enthalpy or, equivalently, the product of the mass flow rate, specific heat capacity, and temperature change. This relationship is fundamental in thermodynamics for calculating the energy required to change the temperature of a fluid in various heating or cooling processes.

$$ Q_C=m_a\left(h_2-h_1\right)=m_a C p m\left(T_2-T_1\right) $$

The different psychrometric processes are shown in following. The chart illustrates the relationship between temperature (t) on the x-axis and humidity ratio (ω) on the y-axis. It is divided into different regions, each representing a specific psychrometric process. The eight main processes shown in the image are:

1. Evaporative Cooling: This process involves cooling the air through the evaporation of water, which decreases the dry-bulb temperature and increases the humidity ratio.
2. Sensible Cooling: This process cools the air without changing its moisture content, resulting in a decrease in the dry-bulb temperature.
3. Sensible Heating: This process heats the air without altering its moisture content, leading to an increase in the dry-bulb temperature.
4. Heating + Humidity: This process involves heating the air while increasing its moisture content, resulting in an increase in both the dry-bulb temperature and the humidity ratio.
5. Cooling + Dehumidification: This process cools the air while reducing its moisture content, leading to a decrease in both the dry-bulb temperature and the humidity ratio.
6. Dehumidification: This process removes moisture from the air without changing its dry-bulb temperature.
7. Humidification: This process adds moisture to the air without changing its dry-bulb temperature.
8. Heating + Humidification: This process involves heating the air while reducing moisture, increasing the dry-bulb temperature and reducing the humidity ratio.

Psychrometric Processes

Sensible Cooling

During this process, the moisture content of air remains constant but its temperature decreases as it passes over a cooling coil. To keep the moisture content constant, the surface of the cooling coil should be dry and its surface temperature should be greater than the dew point temperature of the air. If the cooling coil is 100% effective, then the exit temperature of the air will be equal to the coil temperature. However, in practice, the exit air temperature will be higher than the cooling coil temperature. Figure below shows the sensible cooling process 2–1 on a psychrometric chart. The heat rejection rate during this process is given by:

Sensible Heating

During Sensible Hating process, the moisture content of air remains constant and its temperature increases as it flows over a heating coil. The heat addition rate during this process is given by:

$$ Q_h=m_a\left(h_2-h_1\right)=m_a c_{p m}\left(T_2-T_1\right) $$

where c_pm is the humid specific heat (≈1.0216 kJ/kg dry air) and m_a is the mass flow rate of dry air (kg/s).

Cooling and Dehumidification

When moist air is cooled below its dew-point by bringing it in contact with a cold surface, some of the water vapor in the air condenses and leaves the air stream as a liquid, as a result, both the temperature and humidity ratio of air decreases as shown. This is the process air undergoes in an air conditioning system. The actual process path depends on the type of cold surface, the surface temperature, and flow conditions, but for simplicity, the process line is assumed to be a straight line as shown in Figure 8.11. The heat and mass transfer rates can be expressed in terms of the initial and final conditions by applying the conservation of mass and conservation of energy equations as given below:

By applying mass balance for the water: $$ m_a \cdot \omega_a=m_a \cdot \omega_2+m_w $$ By applying energy balance: $$ m_a \cdot h_a=Q_r+m_w \cdot h_w+m_a \cdot h_2 $$ From the above two equations, the load on the cooling coil, $Q_t$ is given by: $$ Q_r=m_a\left(h_1-h_2\right)-m_a\left(\omega_1-\omega_2\right) h_w $$

The 2^nd term on the RHS of the above equation is normally small compared to the other terms, so it can be neglected. Hence,

$$ Q_r=m_a\left(h_1-h_2\right) $$

It can be observed that the cooling and de-humidification process involves both latent and sensible heat transfer processes, hence, the total, latent and sensible heat transfer rates (Q_r, Q_l, and Q_s) can be written as:

$$ \mathrm{Q}_{\mathrm{r}}=\mathrm{Q}_1+\mathrm{Q}_{\mathrm{s}} $$ where $$Q_1=m_a\left(h_1-h_w\right)=m_a \cdot h_{f g}\left(\omega_1-\omega_w\right)$$ and $$Q_s=m_a\left(h_w-h_2\right)=m_a \cdot c_{p m}\left(T_1-T_2\right)$$

Sensible Heat Factor (SHF)

It is defined as the ratio of sensible to total heat transfer rate (Q_t), i.e.,

$$ \mathrm{SHF}=\mathrm{Q}_{\mathrm{s}} / \mathrm{Q}_{\mathrm{t}}=\mathrm{Q}_{\mathrm{s}} /\left(\mathrm{Q}_{\mathrm{s}}+\mathrm{Q}_{\mathrm{l}}\right) $$

From the above equation, we can observe that an SHF of 1.0 corresponds to no latent heat transfer and an SHF of 0 corresponds to no sensible heat transfer. An SHF of 0.75 to 0.80 is quite common in air conditioning systems in a normal dry-climate. A lower value of SHF, say 0.6, implies a high latent heat load such as that occurs in a humid climate.

The temperature, Ts, is the effective surface temperature of the cooling coil and is known as apparatus dew-point (ADP) temperature. In an ideal situation, when all the air comes in perfect contact with the cooling coil surface, then the exit temperature of the air will be same as ADP of the coil. However, in the actual case, the exit temperature of the air will always be greater than the apparatus dew-point temperature due to boundary layer development as air flows over the cooling coil surface and also due to temperature variation along the fins, etc. Hence, we can define a by-pass factor (BPF) as it can be easily seen that higher the by-pass factor larger will be the difference between air outlet temperature and the cooling coil temperature. When BPF is 1.0, all the air bypasses the coil and there will not be any cooling or de-humidification.

$$ \mathrm{BPF}=\frac{T_c-T_s}{T_a-T_s} ; \mathrm{CF}(\text { Contact Factor })=1-\mathrm{BPF} $$

Where T_c temperature of air leaving, T_a is temperature of air entering and T_s is temperature of surface of cooling coil.

Heating and Humidification

During winter it is essential to heat and humidity the room air for comfort. This is normally done by first sensible heating the air and then adding water vapor to the air stream through steam nozzles.

Mass balance of water vapor for the control volume yields the rate, at which steam has to be added, i.e., m_w:

$$ m_w=m_a\left(\omega_2-\omega_1\right) $$

where m_a is the mass flow rate of dry air. From energy balance:

$$ Q_h=m_a\left(h_2-h_1\right)-m_w h_w $$

where Q_h is the heat supplied through the heating coil and h_w is the enthalpy of steam. Since this process also involves simultaneous heat and mass transfer, we can define a sensible heat factor for the process in a way similar to that of a cooling and dehumidification process.

Cooling and Humidification

As the name implies, during this process, the air temperature drops and its humidity increases. This can be achieved by spraying cool water in the air stream. The temperature of the water should be lower than the dry-bulb temperature of air but higher than its dew-point temperature to avoid condensation (T_DPT < T₂ < T₁).

During this process, there is sensible heat transfer from air to water and latent heat transfer from water to air. Hence, the total heat transfer depends upon the water temperature. If the temperature of the water sprayed is equal to the wet-bulb temperature of the air, then the net transfer rate will be zero as the sensible heat transfer from air to water will be equal to latent heat transfer from water to air. If the water temperature is greater than WBT, then there will be a net heat transfer from water to air. If the water temperature is less than WBT, then the net heat transfer will be from air to water. Under a special case when the spray water is entirely recirculated and is neither heated nor cooled, the system is perfectly insulated and the make-up water is supplied at WBT, then at steady-state, the air undergoes an adiabatic saturation process, during which its WBT remains constant. This is the process of adiabatic saturation. The process of cooling and humidification is encountered in a wide variety of devices such as evaporative coolers, cooling towers, etc.

Heating and Dehumidification

This process can be achieved by using a hygroscopic material, which absorbs or adsorbs the water vapor from the moisture. If this process is thermally isolated, then the enthalpy of air remains constant, as a result, the temperature of air increases as its moisture content decreases. This hygroscopic material can be a solid or a liquid. In general, the absorption of water by the hygroscopic material is an exothermic reaction, as a result heat is released during this process, which is transferred to air and the enthalpy of air increases.