Infiltration Simplified Models – LBNL Model

As discussed previously, it is straightforward to calculate the air exchange rate of a given building if (1) the location and leakage function for every opening in the building

envelope are known, (2) the wind pressure coefficients over the entire building envelope for a given time throughout the year are known, and (3) any mechanical ventilation airflow rates are known. Generally speaking these inputs are unavailable for most buildings except very simple structures or extremely well studied buildings. Therefore, much work has been done to provide accurate models for air infiltration. Several

procedures have been developed to calculate building air exchange rates that are based on physical models of the building interior as a “single zone.” Single zone approximations are to be used for buildings that have low internal resistance to airflow (like this test home). These models are not likely to return accurate results for large, multi-zone buildings (such as high-rise or commercial structures). Single zone models have been developed by the Institute of Gas Technology (IGT), the Building Research

Establishment, and the Lawrence Berkeley National Laboratory (LBNL) [18].

The last model is referred to as the “LBNL model” and is widely used as a basis for residential air exchange calculations. The LBNL model originally was designed to use building pressurization test data results to characterize home air leakage through the “effective leakage area” (AL) at a 4 Pa test pressure, but later was modified to use the calculated “building air leakage area” (“Ac”Discussed in the Air Leakage Section of this report). The LBNL model takes into account outside wind speed and temperature as well as certain building parameters called the “Stack Coefficient” (Cs), and the “Wind

Coefficient” (Cw).

The Stack Coefficient (referring to the “stack effect” as an infiltration driving mechanism) is a simple value to determine. The various values of the Stack Coefficient are shown in Table 4.3 for various building heights (building stories / levels). For the LBNL model, house heights of one-, two-, and three-story buildings are taken as 2.5, 5.0, and 7.5 meters respectively. The Stack Coefficient has units of (L/s)2/[(cm4)*K].

Determining the LBNL model Wind Coefficient (Cw) is a two step process. First, a building “Local Shielding Class” must be determined. The Local Shielding Class is based on the surroundings of the building in question. Various peripheral obstacles such as trees, adjacent buildings and solid fences play a role in distorting the incident wind on the exterior of a building and the Local Shielding Class takes these objects into account.

Table 4.4 shows the various Local Shielding Classes for residential homes. Local Shielding Class 4 is taken as the “typical suburban” setting while class 5 is taken as a “typical downtown” setting. Once a shielding class is known, a Wind Coefficient can be determined. The Wind Coefficient is a function of both the Local Shielding Class and the building height (stories/levels). Typical Wind Coefficient values are shown in Table 4.5 for various combinations of shielding class and building heights. The Wind Coefficient has units of (L/s)2/[(cm4)*(m/s)2].

Table 4.3: Stack Coefficient Cs

House Height (Stories)

One Two Three

Stack Coefficient 0.000145 0.00029 0.000435

Table 4.4: Local Shielding Classes

Class Description

1 No obstructions or local shielding

2 Light local shielding; few obstructions, few trees, or small shed 3 Moderate local shielding; some obstructions within two house

heights, thick hedge, solid fence, or one neighboring house

4

Heavy shielding; obstructions around most of perimeter,

buildings or trees within 10 m in most directions; typical suburban shielding

5

Very heavy shielding; large obstructions surrounding perimeter within two

Table 4.5: Wind Coefficient Cw

Shielding House Height (stories)

Class One Two Three

1 0.000319 0.00042 0.000494 2 0.000246 0.000325 0.000382 3 0.000174 0.000231 0.000271 4 0.000104 0.000137 0.000161 5 0.000032 0.000042 0.000049

Once the Stack Coefficient, Wind Coefficient, inside temperature conditions, outside weather conditions (wind speed and outside temperature), and effective air leakage area (or calculated building air leakage area) for a particular building are known, the airflow rate into (or out of) that building can be calculated using the LBNL model equation:

Q = (AL/1000) * [CsΔt + CwV2](1/2)

The airflow rate (Q) has units of m3/s, the Stack Coefficient (Cs) has dimensionalized units of (L/s)2/[(cm4)*K], the Wind Coefficient (Cw) has

dimensionalized units of (L/s)2/[(cm4)*(m/s)2], the average outside wind speed (V) at a given instant in time has units of m/s, and the average indoor-outdoor temperature different (Δt) for a given instant in time is measured in units of Kelvin. The building leakage area (AL) is typically a measured value having units of cm2, but a calculated effective air leakage area (ELA) value or building air leakage area (Ac) value can be used interchangeably [18].

As discussed in the “Basics Concepts” section of this report, the air exchange rate (I) of the building is obtained by dividing the air flow rate (Q from above) by the building volume (V). If the time interval in the calculation is for 1 hour (typical for weather station data) then this air exchange rate becomes the often used Air Changes per Hour (ACH) value. A calculation such as this gives the amount of outside air that is entering or leaving the building in question. This allows an estimate of the HVAC energy (power)

that will be required to condition the “infiltrating” outside air to acceptable inside comfort levels.

The predictive accuracy of the LBNL model can be very good. The LBNL model can be as accurate as +/- 7% for weekly value and +/- 20% for “short term” calculations when the building parameters are well known (Sherman and Modera 1986).