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Wind-driven air infiltration has been recognized among the major reasons for energy loss in buildings, and the impact to energy efficiency under steady conditions has been reported and issued as part of many building codes. The nearly zero-energy building demand makes uncontrolled leakage paths even more undesired and creates the need for further investigation of their behavior under unsteady wind conditions. The present numerical study examines the role of wind gustiness on instantaneous infiltration rates of a low-rise building. For this purpose, two levels of gust frequency Ω have been simulated, expressed as a sinusoidal factor in the wind profile formula. In parallel, a ratio α is employed to represent seven different cases of external leakages distribution, while five scenarios of compartmentalization and internal leakages shows the impact of the latter on the dynamics of building air exchange rates. The results indicate that higher wind gustiness results in higher ACH, marking out gusts as a potential critical factor under unsteady climate conditions. The infiltration rates shown in relation to the leakage distribution ratio α provide arguments for the importance of the detailed detection of external leakages while the comparison of the different internal-volume-scenario highlights the key-role of internal leakages control towards a drastic reduction of infiltration rates.

Air infiltration in buildings refers to the uncontrolled or unintentional flow of outside air to the internal space through leakages in the envelope, typically cracks and/or large leakage points. From the 1970s onwards, its impact on energy performance has been recognized in the literature, e.g., [

Air infiltration in buildings can be driven either by the wind-induced pressure differences across the envelope or by the gradients between internal and external temperatures (buoyancy pressures) or by the mechanical ventilation [

Physical models of the driving forces and their interaction with the building have been presented in order to estimate infiltration rates, based on the leakage numbers and climate indicators [

However, especially in low-rise buildings, wind gustiness and the consequent pressure gradient on the facades seem to govern the air exchanges [

The dynamic characteristics of air infiltration was very early pointed out by Hill and Kusuda [

In addition, leakage distribution has been mentioned as an important factor affecting the infiltration/ventilation rates [

The paper focuses on wind-driven infiltration (buoyancy pressures are neglected and no mechanical ventilation system has been applied). Its major objective is to ascertain the influence of wind unsteadiness in the instantaneous infiltration rates through a transient analysis. In particular, the impact of wind gust frequency on the air in- and exfiltration rates of a cross-ventilated building-model with variable leakage areas. The role of the internal leakages is also studied and for this reason five different compartmentalization/partition-wall-permeability scenarios are researched. A computational fluid dynamics (CFD) solver that has been widely used in estimation of cross ventilation rates (SST k-ω) is employed. The unsteady conditions (wind gust frequencies) are simulated as an additional sinusoidal factor in the wind profile formula. The accumulated infiltration rates over one hour (ΣACH) are calculated for the two wind gust frequencies cases, proving the potential of higher gustiness to create higher air exchange rates (ACH).

The current numerical study deals with the influence of unsteady wind to the instantaneous air exchange rates of a one-story low rise building. The geometry of the parallelepiped model is 10 m × 3 m × 5 m (

(

As mentioned above, the main objective of this paper is to research the impact of the wind gust frequency. The investigation of the role of the latter is important towards the estimation of the wind-driven infiltration of a building in operation. In this context, two gust frequencies, Ω_{high} = 0.5 Hz and Ω_{low} = 0.1 Hz, are assumed, while they are implemented in the logarithmic wind profile formula as an additional sinusoidal factor. The wind speed fluctuates in all the frequencies between 0.0005 and 5 Hz [

In order to study the role of the internal leakages, five scenarios (S_{1–5}) are employed (_{1} refers to a single-room model (without any partition wall), while in all the other cases refer to compartmentalized volume. The cases S_{2}, S_{3}, S_{4} and S_{5} represent different “permeability” of the partition wall in terms of internal leakages. In all the cases, the internal leakages are located on the lower level of the partition wall. In the scenarios S_{2}, S_{3}, and S_{4}, different amounts of leakages are simulated, while in the last one (S_{5}), the assumption of a completely tight wall is employed.

The total external leakage area of the building envelope is selected as 128 cm^{2}, which is approximately equal to 0.01% of the total exposed model surface. The leakages are located on the windward and on the leeward facade of the building, while no leakage paths are assumed to be on its sides. In order to research the influence of the leakage distribution under unsteady wind conditions and to see their physical connection to the internal leakages, seven cases of leakage distribution are solved. For the representation of the distribution of the external leakages on the windward and the leeward side, a ratio α is defined as follows:
_{leak,windward} is the area of the leakages located on the windward side of the building and _{leak,total} the total leakage area, the sum of the leakages on the windward and the leeward side (=128 cm^{2}). In fact, the ratio α expresses the portion of the envelope leakages that is located on the windward side. The α takes the values: α = 5%, α = 15%, α = 30%, α = 50%, α = 70%, α = 85% and α = 95%.

The simulated building is surrounded by a fetch which plays the role of the domain. The size of the domain is 70 m × 18 m × 40 m. In order to deal with license constraints and to increase the number of the elements used in the mesh and consequently the accuracy of the solver, a symmetry plane has been used. An unstructured mesh of approximately 1.9 × 10^{6} elements (1.4 × 10^{6} tetrahedral, 1 × 10^{4} pyramids, 4 × 10^{5} prisms) and 4.6 × 10^{5} nodes has been used.

Internal leakages scenarios (S_{1−5}). Partition wall and internal leakages.

Scenario | Partition Wall | Internal Leakages |
---|---|---|

Scenario S_{1} |
No | – |

Scenario S_{2} |
Yes | 8 cm^{2} (6.25%) * |

Scenario S_{3} |
Yes | 4 cm^{2} (3.125%) * |

Scenario S_{4} |
Yes | 2 cm^{2} (1.5625%) * |

Scenario S_{5} |
Yes | 0 |

* percentage of the building external surface area.

The computational fluid dynamics package ANSYS CFX was used for the numerical simulations. The Shear-Stress-Transport (SST) model, a two Equation k-ω based model [

At the inlet of the domain, a logarithmic wind profile [_{*} is the shear velocity, _{0} the roughness length and Ψ _{m }a stability function. The stability function can be evaluated directly from the Monin and Obukhov length _{m }and

The second term in the right side of the equation describes the “unsteadiness” of the wind, expressed by the gust frequency Ω. As mentioned above, two gust frequencies Ω have been simulated; Ω_{high} = 0.5 Hz (high frequency) and Ω_{low} = 0.1 Hz (low frequency). The periods ^{−1}. For the steady state (no gust) conditions, the wind velocity is 5.27 m·s^{−1}. The wind direction angle is normal to the windward side of the building, in all the simulated cases.

Variation of velocity

To obtain the dynamics of the building air exchange, the simulations are solved in transient mode. After a mesh sensitivity analysis, a time-step of 0.05 s has been investigated as sufficient for the length and time scale calculations. The instantaneous mass flow rate _{m} is solved numerically and consequently the instantaneous volumetric flow rates _{v}_{tot} = 1 h is calculated:
_{run} is the total run time per case and

In order to have a magnitude of order of the airtightness level of the building-model, an additional case of simulating a 50 Pa pressure difference across the envelope was also performed. Establishing a pressure difference of 50 Pa across the envelope (e.g., using a fan), between indoors and outdoors, has been recognized as a simple and efficient way to characterize the global airtightness of a building, e.g., [_{1}) are shown in the _{50} ≤ 1.5 h^{−1} or _{50,small} ≤ 2.5 h^{−1} for small houses). The CFD pressurization results vary with the leakage distribution ratio α because a change of the magnitude of the leakage area cause a change of the flow conditions (flow exponent, flow coefficient), resulting in a slightly different flow rate.

The maximum allowed air exchanges per hour (ACH) at 50 Pa pressure difference for different kinds of buildings and the respective result from the CFD-simulated pressurization situation for the building-model of this study.

The equivalent air change rates ΣACH against the leakage ratio α for the scenarios S_{1}, S_{2}, S_{3}, S_{4} and S_{5} are shown in _{high}, while the dashed one represents the cases under the low frequency Ω_{low}. It would be reasonable to claim that the gust frequency of the wind has a significant role, altering the infiltration rates of a building in operation. In addition, the leakage distribution seems that could potentially cause large differences in the ACH of an enclosure.

The equivalent air change rate ΣACH respect to the leakage distribution α for the scenario of the single-room building (no partition wall, Scenario S_{1}).

The equivalent air change rate ΣACH respect to the leakage distribution α for the scenarios of compartmentalized volume and internal leakages on the partition wall. (^{2} (Scenario S_{2}); (^{2} (Scenario S_{3}); and (^{2} (Scenario S_{4}).

The ΣACH of the two rooms for Scenario S_{5}, when separated by a totally tight (impermeable) partition wall.

Employing the assumption that the internal volume is single-spaced, _{high} the ACH is 2.73 h^{−1}, while for the low frequency Ω_{low} the rates are 1.31 h^{−1}. For the steady state conditions, the maximum ACH is 0.35 h^{−1}. In contrast, the air exchange rates appear to have the lowest values when the external leakages are located either on the windward (α = 95%) or on the leeward facade of the building (α = 5%). Again, the ΣACH increases in respect to the ratio α until it reaches the maximum value for α = 50% (5% ≤ α ≤ 50%) and then it is getting lower as α increases more (50% ≤ α ≤ 95%). The picture is similar for the steady state conditions (_{1}. Employing the analogy between the air flow in the “enclosure” and a pneumatic spring system and based on the relatively high ACH rates, it would be reasonable to claim that the damping is relatively low. Nevertheless, based on the fairly symmetric picture of the

Moreover, _{high} (0.5 Hz) results in higher equivalent air change rates ΣACH compared to the lower one (0.1 Hz) that was employed for this study. Again, when the period _{low} = 10 s to _{high} = 2 s), the ACH increases. _{1}, depending on how the leakages are distributed in the envelope, the rates alter in a range that varies between 97% (for α = 95%) and 160% (for α = 15%).

The increase of ΣACH for the different leakage-distribution cases when the gust frequency increases from 0.1 to 0.5 Hz.

Scenario | Increase of ΣACH | ||||||
---|---|---|---|---|---|---|---|

α = 5% | α = 15% | α = 30% | α = 50% | α = 70% | α = 85% | α = 95% | |

Scenario 1 | 119% | 160% | 150% | 108% | 97% | 99% | 97% |

Scenario 2 | 103% | 98% | 97% | 99% | 91% | 82% | 80% |

Scenario 3 | 163% | 170% | 171% | 114% | 98% | 98% | 96% |

Scenario 4 | 114% | 90% | 90% | 109% | 104% | 105% | 105% |

Scenario 5 | 59% | 47% | 40% | 52% | 50% | 46% | 46% |

The results show that the leakage distribution can cause large variations in ACH rates, especially under unsteady wind conditions. _{1}, the standard deviation is high, as σ = 0.936 and σ = 0.446 for the Ω_{high} and Ω_{low}, respectively, implying the important influence of the leakage distribution on the air exchange rates of a building in operation. Especially for the high gust frequency, it would be reasonable to claim that the leakage distribution raises an uncertainty issue for the estimation of the realistic infiltration rates of a building.

The standard deviation σ of ΣACH and the respective arithmetic mean when the ACH is considered in respect to the leakage distribution α.

Scenario | Standard Deviation σ (and the Arithmetic Mean) of ΣACH | ||
---|---|---|---|

Ω_{high} |
Ω_{low} |
No Gust | |

Scenario 1 | 0.936 (1.435) | 0.446 (0.661) | 0.121 (0.188) |

Scenario 2 | 0.141 (0.406) | 0.073 (0.211) | 0.012 (0.059) |

Scenario 3 | 0.017 (0.213) | 0.014 (0.094) | 0.002 (0.032) |

Scenario 4 | 0.004 (0.131) | 0.004 (0.065) | 0.002 (0.019) |

Scenario 5 | 0.019 (0.053) | 0.013 (0.036) | 0.001 (0.002) |

Starting with Scenario S_{2}, all the cases presented hereinafter refer to a model in which a partition wall has been added. In total, there are four scenarios with compartmentalized models. In particular, in three of them (S_{2}, S_{3} and S_{4}), internal leakages have been assumed on the partition wall. In _{2}, S_{3} and S_{4} are shown in respect to the leakage distribution ratio α.

It would be reasonable to claim that the existence of a relatively tight partition wall has a drastic impact (drop) on the air change rates (_{high} and Ω_{low}) to be much lower compared to Scenario S_{1}). Although a “cross ventilation” takes place even in those cases (in analogy to S_{1}), the level of tightness of the wall in combination with the inertia forces of the mass of the internal volume increases the damping, resulting in significantly lower infiltration rates. Nevertheless, the impact of the wind gust frequency is important (as in Scenario S_{1}) in all the cases presented in this section (_{1} (

As mentioned above, the partition wall and the compartmentalization of the initial enclosure reduces dramatically the ACH. Scenario S_{2} represents the model with a partition wall on which internal leakages of 8 cm^{2} have been simulated. The rates have been calculated as ΣACH = 0.51 h^{−1} and ΣACH = 0.26 h^{−1} for the Ω_{high} and the Ω_{low}, respectively, while for the steady state no-gust conditions ΣACH = 0.07 h^{−1} (_{1}. The maximum values occur when α = 50% and α = 70% for the high and low gust frequencies, respectively. The internal leakages result in a similar symmetrical picture regarding the equivalent air exchanges; the lowest values of ΣACH occur when the external leakages are concentrated either on the windward or on the leeward facade of the building (α = 95% or α = 5%, respectively). However, the standard deviation is much smaller in this case, implying a more “mild” impact of the leakage distribution on the ACH (

A further reduction of the internal leakages on the partition wall results in an even larger drop of the ACH. In Scenario S_{3} the internal leakages have been scaled down to 4 cm^{2}, half than in the previous Scenario S_{2}. Now the maximum values of the rates have been calculated as ΣACH = 0.23 h^{−1} and ΣACH = 0.11 h^{−1} for the Ω_{high} and the Ω_{low}, respectively, and ΣACH = 0.03 h^{−1} for the no-gust wind conditions (_{3}, as shown in

Finally, by controlling the internal leakages even more and reducing them to 2 cm^{2}, a further reduction of the ACH is achievable. In particular, in Scenario S_{4}, the maximum infiltration rates are ΣACH = 0.14 h^{−1} and ΣACH = 0.07 h^{−1} for the Ω_{high} and the Ω_{low}, respectively, while ΣACH = 0.02 h^{−1} for the steady state conditions (_{3} and S_{4}. Based on _{2}, the infiltration rates do not vary significantly. An exception can be reported for the extreme cases of α = 95% and α = 5%, which are very close to a single-side ventilation situation and, hence, it is not now only the pressure difference between windward and leeward side that matters but also the absolute magnitude on each side.

In contrast, the frequency affects the air exchanges, as there is an increase in the ACH that increases from 96% to 114% when the frequency switches from 0.1 to 0.5 Hz. Under mild wind gust frequency conditions, the relatively tight partition element could potentially result in low air change rates. Thus, internal leakages and wind gust frequency seem to be critical parameters for the estimation of the operational wind-driven infiltration rates of a building.

The role of the internal leakages on the air exchange rates estimation becomes even clearer in Scenario S_{5}. In this case, a hypothesis of a totally tight partition wall is employed. In ^{−1} and ΣACH = 0.05 h^{−1} for the Ω_{high} and the Ω_{low}, respectively, while for the no-gust steady state conditions ΣACH = 0.005 h^{−1} (

The rates increase in respect to the leakage distribution ratio α, so that the maximum values of ACH take place when the leakages are mostly located on the windward facade of the model (α = 95%). The latter is reflected in the standard deviations σ of the rates, which are higher than the respective ones in Scenario S_{4} and fairly equal to those of Scenario S_{3} (

The tight partition wall results in the total compartmentalization of the volume into two spaces. The inertia forces of the mass of the windward “room” are in this case higher because of the single-side infiltration and the compressibility of the volume decreases. The second “room” has gotten “isolated” in this case, so there is not significant air exchange through the leeward leakages. The combination of those facts leads to the dramatic drop of the rates as shown in the

If the leakages are mostly located on the leeward facade or even equally distributed between the windward and the leeward side of the building, the operational air is exchanged, especially under the low gust frequency Ω_{low}. Nevertheless, even for the Ω_{high} the infiltration rates are now lower, implying that a high control of internal leakages can significantly contribute to eliminating the impact of the gust frequency. According to Jones

Finally, _{high}, the low frequency Ω_{low} and the no-gust steady state conditions, in all the scenarios of compartmentalization/partition-wall-permeability. The values of the leakage distribution ratio α to that of when the max and min values occur are given in parenthesis.

The max and min values of ΣACH for Ω_{high}, Ω_{low} and the steady state conditions.

max and min ΣACH | ||||||
---|---|---|---|---|---|---|

Scenario | Ω_{high} |
Ω_{low} |
Steady state, no gust | |||

max | min | max | min | max | min | |

Scenario 1 | 2.73 (50%) | 0.33 (5%) | 1.31 (50%) | 0.15 (5%) | 0.35 (50%) | 0.05 (5%) |

Scenario 2 | 0.51 (50%) | 0.12 (5%) | 0.26 (70%) | 0.06 (5%) | 0.07 (50%) | 0.04 (5%) |

Scenario 3 | 0.23 (30%) | 0.19 (95%) | 0.11 (70%) | 0.07 (5%) | 0.04 (30%) | 0.03 (5%) |

Scenario 4 | 0.14 (50%) | 0.12 (5%) | 0.07 (95%) | 0.06 (5%) | 0.02 (95%) | 0.015 (5%) |

Scenario 5 | 0.08 (95%) | 0.03 (5%) | 0.05 (95%) | 0.02 (5%) | 0.005 (95%) | 0.001 (5%) |

A low rise building with variable leakage areas on the windward and the leeward side was simulated and studied numerically under unsteady wind conditions. The wind-driven infiltration rates under two different wind gust frequencies were calculated and compared to steady state conditions. The gust frequency seems to be a critical parameter, as it results in an increase of air exchanges of a building in operation.

The leakage distribution affects the infiltration rates especially in the single-compartment scenario, where strong cross “ventilation” takes place. The most severe situation appears when the leakage areas on the windward and the leeward facade are of the same magnitude of order. Again, the more equal the leakages are, the higher the distribution of air exchanges.

The existence of relatively tight internal walls in a double-compartment building decreases drastically the infiltration rates, compared to the single-space model. In particular, controlling the internal leakages, the drop of the ACH becomes significant, resulting in rates that could be considered as “acceptable” in a building-regulations context. In those cases, the influence of the gust frequency is still very important, while the role of the leakage distribution is moderate. By creating more tightness in the partition wall, the ACH decreases even more, constraining the impact of the gust frequency.

Leakage distribution creates uncertainty in the estimation of wind-driven infiltration. In addition, the wind gust frequency causes significant variations in the ACH of a building in operation. The paper also highlights that the control of the internal leakages should be a parameter more deeply studied. In decreasing the infiltration rates, the “component” of the internal leakage paths should also be considered as important, as well as the leakages of the envelope. Furthermore, fulfilling a sufficient airtightness level of the internal building elements could also moderate the impact of wind gust frequency.

The study raises issues regarding uncontrolled leakages in the building envelope. The detection of leakages and their distribution ought to be considered as critical factors, while wind unsteadiness results in significant variations in wind-driven infiltration. Furthermore, internal leakages seem to play an important role in the nearly zero-energy building target. Further research needs to be done in order to investigate the connection between internal and external leakages in a more detailed way.

The current study has been financed by the Norwegian University of Life Sciences under project number 12351027.

The authors declare no conflict of interest.

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