Infiltration Loads Methods

Infiltration through doorways represents one of the most significant and variable cooling loads in refrigerated facilities. Air exchange introduces both sensible and latent heat loads, with moisture deposition on evaporator coils creating additional operational challenges through increased defrost frequency and energy consumption.

Door Opening Infiltration

Basic Infiltration Equation

The sensible and latent heat transfer through an open doorway depends on the density difference between inside and outside air:

Sensible Heat:

Qs = 0.221 × A × h × ρo × Fm × (1 - E) × Δh_sensible

Latent Heat:

Ql = 0.221 × A × h × ρo × Fm × (1 - E) × Δh_latent

Where:

• Qs = sensible heat gain, Btu/h
• Ql = latent heat gain, Btu/h
• A = door area, ft²
• h = door height, ft
• ρo = density of outside air, lb/ft³
• Fm = density factor (flow rate multiplier)
• E = effectiveness of protective device (0 to 1.0)
• Δh_sensible = enthalpy difference (sensible), Btu/lb
• Δh_latent = enthalpy difference (latent), Btu/lb

Density Factor (Fm)

The density factor accounts for the actual air exchange rate based on temperature difference:

For temperatures above 0°F:

Fm = 0.8 × (1 - ρi/ρo)^0.5

For temperatures below 0°F:

Fm = 1.1 × (1 - ρi/ρo)^0.5

Where:

• ρi = density of inside air, lb/ft³
• ρo = density of outside air, lb/ft³

Door Opening Frequency Method

The total daily infiltration load depends on door usage patterns:

Q_total = Qs × t_open × n_openings / 24

Where:

• Q_total = average hourly load, Btu/h
• Qs = instantaneous infiltration load, Btu/h
• t_open = average door open time per opening, hours
• n_openings = number of door openings per day

Typical Door Open Times:

Traffic Door Usage Factor

For high-traffic doors, apply a usage factor to account for door efficiency:

Q_design = Q_infiltration × UF × DF

Where:

• UF = usage factor (1.0 to 1.5 for heavy traffic)
• DF = door factor (1.0 for manual, 0.8 for automatic, 0.6 for high-speed)

Gosney-Olama Equation

The Gosney-Olama equation provides a more accurate prediction of infiltration flow rate through vertical openings based on pressure differential:

v = Cd × [2 × g × h × (ρo - ρi) / (ρo + ρi)]^0.5

Where:

• v = average air velocity through opening, ft/s
• Cd = discharge coefficient (typically 0.65 to 0.75)
• g = gravitational acceleration, 32.2 ft/s²
• h = height of opening, ft
• ρo, ρi = outside and inside air density, lb/ft³

Volume Flow Rate:

Q_volume = v × A × 3600 / 2

Where:

• Q_volume = volumetric flow rate, ft³/h
• A = opening area, ft²
• Factor of 2 accounts for bidirectional flow

Mass Flow Rate:

m_dot = Q_volume × ρ_avg / 60

Where:

• m_dot = mass flow rate, lb/min
• ρ_avg = (ρo + ρi) / 2

Discharge Coefficient Values

Air Curtain Effectiveness

Air curtains reduce infiltration by creating a high-velocity air stream across the door opening. Effectiveness depends on air velocity, width coverage, and temperature differential.

Air Curtain Performance

Effectiveness Factor:

E = 1 - (Q_actual / Q_no_curtain)

Where:

• E = effectiveness (0 to 1.0)
• Q_actual = infiltration with air curtain, Btu/h
• Q_no_curtain = infiltration without protection, Btu/h

Required Air Velocity:

v_jet = K × [g × h × (ρo - ρi) / ρi]^0.5

Where:

• v_jet = air curtain discharge velocity, ft/s
• K = velocity factor (1.5 to 2.0 for adequate performance)
• Other terms as previously defined

Air Curtain Design Parameters

Recirculated Air Curtains:

For non-heated air curtains (recirculating cold room air):

Air Curtain Limitations

Air curtain effectiveness decreases with:

• Cross winds >200 fpm (reduce effectiveness by 20-40%)
• Height >10 ft (reduce effectiveness by 5% per additional foot)
• Width >12 ft (use multiple units for wider openings)
• Extended door open periods >5 minutes (effectiveness drops to 40-50%)

Strip Curtain Systems

Flexible strip curtains provide a physical barrier while allowing personnel and equipment passage.

Strip Curtain Infiltration Reduction

Q_strip = Q_open × (1 - η_strip) × F_overlap

Where:

• Q_strip = infiltration with strip curtain, Btu/h
• Q_open = infiltration with open door, Btu/h
• η_strip = strip curtain efficiency
• F_overlap = overlap factor (typically 1.0 to 1.2)

Strip Curtain Efficiency

Strip Curtain Design Considerations

Strip Width Selection:

Overlap Configuration:

• 50% overlap: strip spacing = 0.5 × strip width
• 100% overlap: strip spacing = 0.33 × strip width
• Edge strips: extend 6-8 inches beyond door frame

Material Thickness:

Vestibule Calculations

Vestibules create a buffer zone that significantly reduces direct infiltration between spaces.

Two-Door Vestibule

The infiltration through a two-door vestibule system:

Q_vestibule = Q_single × F_vestibule

Where F_vestibule depends on door operation mode:

Vestibule Volume and Mixing

Minimum Vestibule Volume:

V_min = Q_volume × t_cycle × SF

Where:

• V_min = minimum vestibule volume, ft³
• Q_volume = volumetric flow rate per opening, ft³/min
• t_cycle = door cycle time, min (typically 0.5-2.0 min)
• SF = safety factor (1.5 to 2.0)

Mixing Factor:

For partial air mixing in vestibule:

Q_actual = Q_theoretical × [1 - (1 - e^(-N))]

Where:

• N = number of air changes during door open period
• e = base of natural logarithm (2.718)

Vestibule Design Requirements

Vestibule Conditioning:

Doorway Infiltration Combined Methods

Multiple protection methods can be combined for maximum effectiveness:

Q_combined = Q_open × (1 - E_air) × (1 - E_strip) × F_vestibule × F_operation

Where:

• E_air = air curtain effectiveness
• E_strip = strip curtain effectiveness
• F_vestibule = vestibule factor
• F_operation = operational factor (door management)

Combined Protection Effectiveness

Infiltration Reduction Strategies

Operational Controls

Door Management:

1. Automatic door closers: Reduce average open time by 30-50%
2. High-speed doors: Open/close in 3-5 seconds vs. 15-30 seconds
3. Traffic scheduling: Batch door openings reduces total open time
4. Interlocked vestibule doors: Prevents simultaneous opening

High-Speed Door Performance:

Design Strategies

Pressure Control:

Maintain slight positive pressure in spaces immediately adjacent to refrigerated areas:

ΔP = ρ × g × h × (To - Ti) / (Ti × 144)

Where:

• ΔP = pressure differential, in. w.g.
• ρ = air density, lb/ft³
• g = 32.2 ft/s²
• h = height, ft
• To, Ti = absolute temperatures, °R
• 144 converts lb/ft² to lb/in²

Recommended Pressure Differentials:

Physical Barriers

Threshold and Seals:

Traffic Flow Management:

n_effective = n_actual / F_batch

Where:

• n_effective = effective number of openings
• n_actual = actual number of openings
• F_batch = batching factor (1.0 for random, 0.3-0.7 for scheduled)

Specialized Applications

Blast Freezer Infiltration:

For blast freezers with rapid air movement:

Q_blast = Q_standard × (1 + v_internal/500)

Where:

• Q_blast = adjusted infiltration load, Btu/h
• v_internal = internal air velocity, fpm
• 500 = normalization factor

Cold Storage with Racking:

Obstruction from racking systems near doors affects infiltration:

Load Calculation Example

Problem: Calculate the infiltration load for a freezer door at -10°F with outside conditions of 80°F DB, 67°F WB.

Given:

• Door: 8 ft wide × 10 ft high
• Average open time: 45 seconds per opening
• Frequency: 100 openings per day
• Protection: Strip curtain (80% efficiency)

Solution:

1. Door area: A = 8 × 10 = 80 ft²

2. Air properties:

   • Outside: ρo = 0.0735 lb/ft³, ho = 31.2 Btu/lb
   • Inside: ρi = 0.0877 lb/ft³, hi = -2.8 Btu/lb (at -10°F, ~90% RH)

3. Density factor:

   Fm = 1.1 × (1 - 0.0877/0.0735)^0.5 = 1.1 × 0.616 = 0.678
   

4. Infiltration without protection:

   Q = 0.221 × 80 × 10 × 0.0735 × 0.678 × (31.2 - (-2.8))
   Q = 0.221 × 80 × 10 × 0.0735 × 0.678 × 34.0
   Q = 3,065 Btu per door opening
   

5. With strip curtain:

   Q_actual = 3,065 × (1 - 0.80) = 613 Btu per opening
   

6. Average hourly load:

   Q_avg = 613 × 100 / 24 = 2,554 Btu/h
   

7. Design load (with 25% safety factor):

   Q_design = 2,554 × 1.25 = 3,193 Btu/h
   

ASHRAE Handbook References

Detailed infiltration calculation methods are provided in:

• ASHRAE Handbook—Refrigeration (2022), Chapter 13: Refrigerated-Facility Design

  • Section on Air Exchange and Infiltration
  • Door infiltration calculation procedures
  • Protection device effectiveness factors

• ASHRAE Handbook—Fundamentals (2021), Chapter 16: Airflow Around Buildings

  • Stack effect calculations
  • Pressure differentials across openings

• ASHRAE Handbook—HVAC Applications (2023), Chapter 51: Refrigerated-Facility Design

  • Practical infiltration load estimation
  • Traffic pattern analysis
  • Combined protection systems

Design Recommendations

1. Always use protective devices on refrigerated space doorways—unprotected doors create excessive infiltration loads

2. Select high-speed doors for high-traffic applications (>50 openings/day)

3. Combine protection methods for freezer applications below 0°F—single methods rarely achieve adequate protection

4. Install air curtains with discharge velocity ≥1.5 times the theoretical infiltration velocity

5. Maintain strip curtains regularly—damaged or missing strips eliminate most protective benefit

6. Size vestibules for actual traffic patterns, not minimum code requirements

7. Monitor door open time with data logging to verify design assumptions and identify training opportunities

8. Apply safety factors of 1.15-1.30 for critical applications or uncertain usage patterns

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