Understanding Infiltration

Introduction

Infiltration is the term used to describe the leakage of outdoor air into the conditioned space of a building. For infiltration to happen, two conditions must exist: a pressure differential between outdoor and indoor air, and a path for the air to leak through. Pressure differentials arise through building pressurization, wind, and stack effect. Leakage paths are created through holes and cracks in the building envelope, such as window perimeters, joints between wall materials, mechanical penetrations such as pipes and ducts exiting or entering the building, and doors.

Accurately quantifying infiltration can be extremely complex, and most designers will opt to choose a conservative estimate for infiltration due to its unpredictability. Most local codes require building materials to be tested for infiltration to ensure that when the building is operational there won’t be excessive energy usage due to leakage.

Infiltration tends to be higher in the winter, and the impact is much larger in the winter due to the larger temperature difference between outdoor and indoor environments. Summer infiltration is often neglected, however in humid climates it must be considered due to the risk of extra humidity causing mold or bacteria growth indoors.

Impact of Infiltration on Heating and Cooling Loads

If the quantity of infiltration is known, the impact on heating and cooling loads can be easily computed. The equation below states the impact of infiltration on the heating load:

$$q_{heat}=Q_{inf} \times C_s \times (T_{in} - T_{out})$$

Where Q_inf is the volumetric flow rate of the infiltration in cfm, C_s is a constant value for sensible heat gain in air. C_s=1.10 at sea level and 50% humidity, but must be adjusted for elevation. The same equation for the impact on the cooling load is:

$$q_{cool}=Q_{inf} \times C_t \times (h_{out}-h_{in})$$

Where C_t is the total heat gain coefficient for air. C_t=4.5 at sea level and must be adjusted for elevation. The letter h in this equation represents the enthalpy of the air; enthalpy must be used here instead of temperature because the humidity difference between inside and outside air plays a significant role during the cooling season.

As shown by these equations, the impact of infiltration on the load calculation increases linearly with both flow rate and temperature differential (or enthalpy differential). Since temperature differential tends to be much large in the winter, and especially in cold climates, more attention is paid to infiltration for heating calculations. Pressure differential due to stack effect is also exacerbated by temperature differential, causing an additional increase in infiltration in the winter.

Calculating Infiltration

Infiltration can be calculated by the general equation:

$$Q_{inf}=A \times C \times \Delta P^n$$

Where A is the effective leakage area of all cracks, C is the flow coefficient, P is the pressure differential between indoor and outdoor air, and n is the crack flow exponent, which typically ranges from 0.4 to 1. Because n is generally below 1, infiltration is a radical function of pressure differential.

The effective leakage area can be calculated from total crack lengths and crack widths, where the crack width is an approximation based on building age, construction quality, and type of fixture. For example, an operable window will have wider cracks than a fixed window or a curtain wall, and a door will almost always have a wider crack than any window. Crack widths tend to range from around $1 \over 64$” (tight, fixed window) to $1 \over 2$” (loose door).

The flow coefficient, C, is a very complicated value to understand, and typically cannot be directly known - it is dependent on the nature of the crack, wall materials, etc. The reason C is shown here is to indicate that infiltration is generally proportional to crack area, all else kept equal.

Instead of determining C directly, the crack width and C can be combined into one value, K, making infiltration a function of crack length instead of crack width. By doing this, common types of windows and doors can be studied so that a value of K can be assigned based on empirical data rather than exact site conditions. This turns the equation above into:

$$Q_{inf}=L \times K \times \Delta P^n$$

Where L is the crack length. This can be computed for each fixture on a wall, since P should be approximately constant for the face of the wall, and K will be constant for the entire crack length of a fixture.

The value of n is also dependent on the characteristics of the crack and is very difficult to know. The ASHRAE Cooling and Heating Load Calculation Manual gives recommended values for K, as well as curve shapes for different values of K. Deconstructing these curves gives a typical value for n at around 0.66 for doors and 0.5 for windows.

Pressure Differential

Pressure differential between indoor and outdoor environments is made up of three parts:

$$\Delta P= \Delta P_w + \Delta P_s + \Delta P_p$$

Where $\Delta P_w$ is the wind pressure, $\Delta P_s$ is the pressure induced by stack effect, and $\Delta P_p$ is the pressure due to mechanical building pressurization. Since $\Delta P_p$ would typically be measured relative to one point outside the building, you must be careful when calculating $\Delta P_w$ and $\Delta P_s$ because they may be the factors that are influencing $\Delta P_p$, and therefore would already be incorporated into the $\Delta P_p$ value. A different way of estimating $\Delta P_p$ would be to make an approximation based on the difference between exhaust and ventilation air in the air handling system.

Wind Pressure

Wind pressure can only be calculated properly if the wind direction is known. Since wind direction changes all the time, incorporating this factor into load calculations can be a nearly impossible task, unless a variety of scenarios of wind direction and speed are considered. Wind pressure is calculated by:

$$\Delta P_w = {{C_p \rho V_w^2}\over {2 g_c}}$$

Where C_p is the pressure coefficient, is the air density, V_w is the wind velocity, and gc is the gravitational constant. ASHRAE provides graphical data on C_p values for different building shapes and sizes as a function of wind direction angle, as well as more detailed information on flow coefficients, wind shelter factors, and wind pressure distribution in the 2021 Fundamentals Handbook, Chapter 24.

Stack Effect

Stack effect is the infiltration and exfiltration of air at opposite ends of a building caused by pressure differences induced by large continuous stacks in the building, such as stairwells and elevator shafts. For a detailed breakdown of stack effect, visit the blog post Understanding Stack Effect by cilcking here.

Stack effect can be calculated using the equation:

$$\Delta P_s={{C_d P_o h g}\over {R_a g_c}}\times ({1 \over T_o}-{1 \over T_i})$$

Where C_d is the draft coefficient, P_o is the outdoor pressure, h is the vertical distance from the neutral level (NPL), g is the gravitational constant, R_a is the gas constant for air, g_c is a dimensional constant ($g_c={32.17}{{lbm\cdot ft}\over {lbf\cdot s^2}}$), T_o is the outdoor temperature and T_i is the indoor temperature. These values will all be known easily except for C_d and h.

The NPL is the point in the building where the indoor pressure is the same as the outdoor pressure.

C_d must be estimated, and is nearly impossible to know exactly - the value typically ranges between 0.65 (modern office buildings with many stairwell doors and elevators) to 1.0 (buildings with no doors or vertical shafts). The 2023 ASHRAE HVAC Applications Handbook, Chapter 4 provides an alternative method for calculating the P_s value, along with a detailed method for determining the neutral pressure level. Calculating the NPL can be a complicated process, and is usually below the halfway point of the building. Locating more doors in lower levels of the building will lower the NPL, and locating openings at the top of the building will raise it. Using vestibule doors and revolving doors can help mitigate the effects that doors will have on the NPL and stack effect in general.

The NPL of a building with n floors can be estimated using the equation below:

$$NPL={{\sum\limits_{i=1}^n {ECA}_i h_i}\over {\sum\limits_{i=1}^n {ECA}_i}}$$

Where ECA_i is the equivalent crack area for floor i and h_i is the height of floor i. This equation will yield an answer that is the floor that the NPL is expected to be on. The ECA value for each floor can be calculated using the following equation:

$$ECA_i={1\over{{1\over \sum(A_F +A_D + A_W)}+{1\over \sum(A_S+A_E)}}}$$

Where A_F, A_D, and A_W are the building envelope crack areas for cracks around the facade, doors, and windows, respectively, and A_S and A_E are the internal crack areas for cracks around the stairwells and elevator shafts, respectively. Determining these values can be difficult and time consuming, and will almost always result in high uncertainty.

Mechanical Building Pressurization

Building pressurization is a value that is determined by the mechanical designer and can differ based on which area of the building is being analyzed and which air handling unit that part of the building is being served by. If building pressure is being monitored and controlled, and the control is accurate enough, then it is possible that the pressure differentials induced by stack effect and wind will be nullified by the carefully controlled building pressure. However, inaccuracies may arise depending on where the pressure sensors are located and how pressurization and control are being achieved.

Conclusion

Accurately calculating infiltration can be a very complex process, and is often not worth the effort. However, steps do exist for estimating infiltration if adequate building information can be obtained. Most designers will simply take a conservative estimate of infiltration and add enough heat to the heating system to ensure proper capacity is available to handle high amounts of infiltration, while simultaneously attempting to ensure that the infiltration is kept to a minimum to prevent the excess energy usage.

As heating systems move more toward heat pumps, making an overly conservative estimate can have additional negative consequences. Since heat pumps rely on a refrigeration cycle for heating, oversizing the equipment will result in loss of efficiency due to the equipment operating below its peak capacity, especially since heating calculations are already overly conservative to begin with. Most methods of reducing infiltration impacts are architectural in nature, especially with regards to mitigating stack effect.