1. What is a Recirculation Rate with Filter Efficiency (Class II System) Calculator?

Definition: This calculator computes the recirculation rate (\( R V_r \)) for a constant air volume (Class II) system with a filter at location A, considering ventilation effectiveness, filter efficiency, and flow reduction factor.

Purpose: It is used in HVAC systems to determine the recirculation rate needed to maintain acceptable indoor air quality while minimizing outdoor air intake, optimizing energy efficiency through effective filtration.

2. How Does the Calculator Work?

The calculator uses the following formula for the recirculation rate:

Recirculation Rate: \[ R V_r = \frac{N + E_v V_o (C_o - C_s)}{E_v E_r E_f C_s} \]

Where:

• \( R V_r \): Recirculation rate (cfm/person, m³/s/person, L/s/person)
• \( N \): Contaminant generation rate (ppm·cfm/person)
• \( E_v \): Ventilation effectiveness (dimensionless, e.g., 0.70 for 70%)
• \( V_o \): Outdoor air rate (cfm/person, m³/s/person, L/s/person)
• \( C_o \): Outdoor contaminant concentration (ppm)
• \( C_s \): Space contaminant concentration (ppm)
• \( E_r \): Flow reduction factor (dimensionless, typically 1 for constant volume)
• \( E_f \): Filter efficiency (dimensionless, e.g., 0.80 for 80%)
• Conversion factor: 0.0283 cfm/(ft³/min) applied to concentration terms for ppm consistency

Unit Conversions:

• Outdoor Air Rate (\( V_o \)): cfm/person, m³/s/person (1 cfm = 0.000471947 m³/s), L/s/person (1 cfm = 0.471947 L/s)
• Recirculation Rate (\( R V_r \)): cfm/person, m³/s/person (1 cfm = 0.000471947 m³/s), L/s/person (1 cfm = 0.471947 L/s)

Steps:

• Enter the contaminant generation rate (\( N \)), ventilation effectiveness (\( E_v \)), outdoor air rate (\( V_o \)), outdoor contaminant concentration (\( C_o \)), space contaminant concentration (\( C_s \)), flow reduction factor (\( E_r \)), and filter efficiency (\( E_f \)), and select units where applicable.
• Convert outdoor air rate to cfm/person.
• Apply the conversion factor to the term \( E_v V_o (C_o - C_s) \).
• Calculate the recirculation rate using the formula (result in cfm/person).
• Convert the result to the selected unit (cfm/person, m³/s/person, or L/s/person).
• Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Recirculation Rate with Filter Efficiency Calculation

Calculating the recirculation rate with filter efficiency is crucial for:

• Indoor Air Quality: Ensures acceptable air quality by determining the recirculation needed to dilute contaminants, considering the filter's ability to remove pollutants.
• Energy Efficiency: Minimizes outdoor air intake, reducing energy consumption for heating or cooling, while maintaining air quality through effective filtration.
• HVAC Design: Helps design Class II constant air volume systems with filters at location A, optimizing ventilation and filtration strategies for occupant health and system performance.

4. Using the Calculator

Examples:

• Example 1: For \( N = 100 \, \text{ppm·cfm/person} \), \( E_v = 0.70 \), \( V_o = 20 \, \text{cfm/person} \), \( C_o = 0 \, \text{ppm} \), \( C_s = 150 \, \text{ppm} \), \( E_r = 1.00 \), \( E_f = 0.80 \), recirculation rate in cfm/person:
  • Conversion factor: 0.0283 cfm/(ft³/min)
  • Numerator: \( N + E_v V_o (C_o - C_s) = 100 + 0.70 \times 20 \times (0 - 150) \times 0.0283 \)
  • \( = 100 + 0.70 \times 20 \times (-150) \times 0.0283 = 100 - 59.43 = 40.57 \)
  • Denominator: \( E_v E_r E_f C_s = 0.70 \times 1.00 \times 0.80 \times 150 \times 0.0283 = 2.3772 \)
  • \( R V_r = \frac{40.57}{2.3772} \approx 17.06449 \)
  • Since 17.06449 < 10000 and > 0.00001, display with 5 decimal places: \( 17.06449 \)
• Example 2: For \( N = 50 \, \text{ppm·cfm/person} \), \( E_v = 0.65 \), \( V_o = 0.01 \, \text{m³/s/person} \), \( C_o = 10 \, \text{ppm} \), \( C_s = 200 \, \text{ppm} \), \( E_r = 1.00 \), \( E_f = 0.90 \), recirculation rate in m³/s/person:
  • Convert: \( V_o = 0.01 \times 2118.88 = 21.1888 \, \text{cfm/person} \)
  • Numerator: \( 50 + 0.65 \times 21.1888 \times (10 - 200) \times 0.0283 \)
  • \( = 50 + 0.65 \times 21.1888 \times (-190) \times 0.0283 \approx 50 - 74.1042 = -24.1042 \)
  • Denominator: \( 0.65 \times 1.00 \times 0.90 \times 200 \times 0.0283 = 3.31155 \)
  • \( R V_r = \frac{-24.1042}{3.31155} \approx -7.27930 \)
  • Result is negative, so display error: "Error: Recirculation rate (\( R V_r \)) cannot be negative! Check input values."
• Example 3: For \( N = 200 \, \text{ppm·cfm/person} \), \( E_v = 0.80 \), \( V_o = 10 \, \text{L/s/person} \), \( C_o = 5 \, \text{ppm} \), \( C_s = 100 \, \text{ppm} \), \( E_r = 1.00 \), \( E_f = 0.85 \), recirculation rate in L/s/person:
  • Convert: \( V_o = 10 \times 2.11888 = 21.1888 \, \text{cfm/person} \)
  • Numerator: \( 200 + 0.80 \times 21.1888 \times (5 - 100) \times 0.0283 \)
  • \( = 200 + 0.80 \times 21.1888 \times (-95) \times 0.0283 \approx 200 - 45.5867 = 154.4133 \)
  • Denominator: \( 0.80 \times 1.00 \times 0.85 \times 100 \times 0.0283 = 1.9234 \)
  • \( R V_r = \frac{154.4133}{1.9234} \approx 80.28784 \, \text{cfm/person} \)
  • Convert to L/s/person: \( 80.28784 \times 0.471947 \approx 37.89298 \)
  • Since 37.89298 < 10000 and > 0.00001, display with 5 decimal places: \( 37.89298 \)

5. Frequently Asked Questions (FAQ)

Q: What is a Class II system in HVAC design?
A: A Class II system in HVAC design refers to a constant air volume system with a filter at location A (typically in the supply air stream), as defined in standards like ASHRAE, focusing on maintaining air quality through recirculation and filtration.

Q: Why is the conversion factor 0.0283 used in the formula?
A: The conversion factor 0.0283 cfm/(ft³/min) adjusts for unit consistency when working with ppm (parts per million) concentrations, ensuring the formula balances the contaminant generation and removal rates appropriately.

Q: How can I determine the contaminant generation rate for my system?
A: The contaminant generation rate (\( N \)) can be estimated based on the sources of pollutants (e.g., occupants, equipment, materials) in the space, often derived from environmental studies, manufacturer data, or air quality measurements, typically normalized per person.

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