Question

Figure P12.5D shows a system for supplying a space with \(2100 \mathrm{~m}^{3} / \mathrm{min}\) of conditioned air at a dry-bulb temperature of \(22^{\circ} \mathrm{C}\) and a relative humidity of \(60 \%\) when the outside air is at a dry-bulb temperature of \(35^{\circ} \mathrm{C}\) and a relative humidity of \(55 \%\). Dampers A and B can be set to give three alternative operating modes: (1) Both dampers closed (no use of recirculated air). (2) Damper A open and damper B closed. One-third of the conditioned air comes from outside air. (3) Both dampers open. One-third of the conditioned air comes from outside air. One- third of the recirculated air bypasses the dehumidifier via open damper B, and the rest flows through the damper A. Which of the three operating modes should be used? Discuss.

Short answer

Choose the mode with the least energy requirement, comparing Q values for each operating mode.

Step-by-step solution

- Calculate the mass flow rate of air

Given the volumetric flow rate of conditioned air is 2100 m³/min. Assume air density to be approximately 1.2 kg/m³. \[ \dot{m} = 2100 \times 1.2 = 2520 \text{ kg/min} \]

- Determine Specific Humidity

Use the properties of air to calculate the specific humidity at given temperatures and relative humidity. You may need psychrometric charts or tables. Let's denote the specific humidity of inside air (\text{conditioned air}) as \(w_{in} \) and outside air as \(w_{out} \).

- Calculate Enthalpy of the air

Calculate the enthalpy of the conditioned air and outside air using enthalpy formulas for moist air. Denote enthalpy of conditioned air as \( h_{in} \) and outside air as \( h_{out} \).

- Evaluate Mode 1 (No recirculated air)

In this mode, all the supply air comes from outside. Use the enthalpy change formula to determine the energy required to maintain desired conditions. \[ Q_{no\text{recirc}} = \dot{m} (h_{out} - h_{in}) \]

- Evaluate Mode 2 (Damper A open, Damper B closed)

In this mode, one-third of the air comes from outside, and two-thirds are recirculated. Calculate the resulting enthalpy: \[ h_{mix} = \frac{1}{3} h_{out} + \frac{2}{3} h_{in} \]The energy required is: \[ Q_{Aopen} = \dot{m} (h_{mix} - h_{in}) \]

- Evaluate Mode 3 (Both dampers open)

In this mode, one-third is from outside, one-third is recirculated bypassing the dehumidifier, and one-third passing through. Calculate the mixture's enthalpy and the resulting energy required. \[ h_{bypass} = \frac{1}{3} h_{out} + \frac{1}{3} h_{in} + \frac{1}{3} h_{dehumid} \]Calculate the energy required: \[ Q_{bothopen} = \dot{m} (h_{bypass} - h_{in}) \]

- Comparison

Compare the energy values calculated in each mode. Choose the mode which requires the least energy Q to maintain the desired conditions.

Key concepts

Specific Humidity Calculation

Specific humidity is a measure to quantify the amount of moisture in the air. It's the mass of water vapor present in a unit mass of dry air. To calculate this, you'll need the dry-bulb temperature and the relative humidity values. Generally, psychrometric charts are used.
For our problem:

• Specific humidity of inside air (conditioned air) can be represented as \(w_{in}\).
• Specific humidity of outside air can be represented as \(w_{out}\).

Using the psychrometric chart corresponding to the given conditions:
For conditioned air at 22°C and 60% relative humidity, find \(w_{in}\).
For outside air at 35°C and 55% relative humidity, determine \(w_{out}\).
Specific humidity is crucial because it’s a conservative property; meaning it does not change unless moisture is added or removed.

Enthalpy of Moist Air

Enthalpy is an essential concept in HVAC systems, representing the total heat content of the air. It is significant for calculating the energy required for heating, cooling, and dehumidifying processes. Enthalpy of moist air combines both the sensible and latent heat.
The formula for enthalpy of moist air:
\[ h = c_{pa}T + w(h_{fg} + c_{pw}T) \]
Where:

• \( h \) = Enthalpy of moist air
• \( c_{pa} \) = Specific heat of dry air (approx. 1.005 kJ/kg°C)
• \( T \) = Temperature in °C
• \( w \) = Specific humidity
• \( h_{fg} \) = Latent heat of vaporization (approx. 2500 kJ/kg)
• \( c_{pw} \) = Specific heat of water vapor (approx. 1.82 kJ/kg°C)

For conditioned air at 22°C and specific humidity \(w_{in}\), find \(h_{in}\).
For outside air at 35°C and specific humidity \(w_{out}\), determine \(h_{out}\).
Knowing the enthalpy helps in evaluating the energy required in each operating mode.

Recirculated Air Modes

Recirculation modes in HVAC systems control how much air is recycled within a building, impacting energy efficiency and air quality. In our example, there are three modes:

• Mode 1 - No Recirculated Air: Here, all the supply air comes from outside, meaning higher energy usage to condition the air.
• Mode 2 - Damper A Open: One-third of air is drawn from outside, the rest is recirculated. This mode combines the benefits of fresh air with lesser energy requirements.
• Mode 3 - Both Dampers Open: A more complex mode where one-third is outside air, one-third is recirculated bypassing the dehumidifier, and the remainder mixes in. This mode offers a balanced approach to energy use and air quality.

Evaluate each mode by calculating the mixture enthalpy and energy required to maintain desired conditions. The goal is to choose the mode that requires the least energy to provide the same level of air comfort.