Investigation On Dynamic Mechanisms Of Aerosol Penetration Through Cracks On Building Walls

Infiltration ventilation is an important way for the exchange of atmosphere and particulate matter indoors and outdoors when the building envelopes like doors or windows are closed.When the extreme haze or dusty weather occurs,or serious accidents such as nuclear and hazardous chemicals leakage that threaten the safty of the people's lives happen,people always choose to close the building envelops to prevent polluted particulate matters from penetrating indoors.However,particulate matter outdoors can penetrate through the cracks on the building walls with the infiltration airflow,which in turn affects the indoor air quality.Because the dynamic mechanisms of aerosol particles penetrating through the cracks on the building walls is not clear,thus,the convective diffusion equation including the gravity is firstly solved,and the particle concentration,mean concentration(penetration rate)and mass transfer coefficient(deposition velocity)in a narrow rectangular channel(model for a building crack)are obtained theoreticaly and analyzed numerically.Secondly,the aerosol penetration rate through a rough(smooth)crack and a multi-bended crack are obtained theoretically,and the influence of differential pressure across the cracks,flow velocity,airflow types,crack configurations on the particle penetration rate are analyzed.The analytical expressions for particle concentration,mean concentration and deposition velocity at the wall are obtained through strict theoretical calculations when particles pass through a horizontal rectangular channel in the laminar flow regime.Based on the analytic results,the aerosol concentrations are analyzed numerically to describe the developing process of the particle concentration profiles quantitatively,and the characteristics of the asymmetric concentration profiles influenced by gravitational settling can be easily found in the present study.Comparing with the previous studies,the solution obtained in this study for simultaneous considering the Brownian diffusion and gravitational settling has a wider range for applications,and the results are more accurate.Based on the infinite series solution,a concise correlation for the aerosol penetration rate due to the Brownian diffusion was obtained by fitting,which is not only simple in form but also accurate in results by comparing with the formulae in literatures.By comparing the results due to the individual mechanism of Brownian diffusion and gravity sedimentation,respectively,the effect of gravity on aerosol deposition can be neglected if the depositional parameter is less than 0.1,and the diffusion is negligible when the depositional parameter is greater than 9.The deposition velocity at the inner wall of the channel decreases with the increase of the dimensionless transport distance,especially a non-monotonic decrease of the deposition velocity is found at the lower wall of the channel with the increase of the non-dimensional distance.The Graetz method is employed to calculate the infinite series coefficients,which improves the calculating efficiency and ensures the accuracy of numerical calculation.Diffusional and gravitational deposition of aerosols from Poiseuille laminar airflow without consideration of axial diffusion in a rectangular channel with an incline angle is studied by strict theoretical analysis.By theoretical calculation,the solutions of aerosol concentration and mean concentration decaying along the airflow direction are obtained,in which three cases of pure diffusion,individual gravity and combined mechanisms under the two airflow types of uphill and downhill airflows are considered.The results show that the mean concentration decreases with the decrease of the Peclet number.When the Peclet number increases(convection becomes obvious),the particle deposition mainly occurs in the downstream area of the channel away from the inlet.The mean concentration at the same position is inversely proportional to the deposition parameter under the two conditions of downhill and uphill airflows.Under the same conditions,the particle mean concentration in a channel with large inclination angle is higher than that with small angle,and it depends obviously on the depositional parameter.The difference between the mean concentrations for two cases of uphill and downhill airflows becomes apparent only if the Peclet number is small and the depositional parameter is large.The aerosol mean concentration corresponding to the uphill airflow at the same position is smaller than that to the downhill flow because of the vertically downward settling velocity.The mean concentrations due to the individual gravitational settling under the uphill and downhill airflows obtained in the present study are in good agreement with the results in literature.The difference between them appears mainly in the case of downhill flow and large dimensionless distance.The study on the critical penetration distance of the aerosol particles shows that the more inclined the channel,the greater the critical penetration distance.In order to fully understand the penetration mechanisms of aerosol particles through a crack with rough inner surface of building envelopes,the rough crack model is proposed,based on the principle of equivalent surface,to solve the practical problem in which the estimation on aerosol penetration by using existing method is not accurate enough.The analytical expression for the penetration rate of the particles due to the combined mechanisms of diffusion and gravity in the Poiseuille flow regime is obtained through strict theoretical deduction.The detailed comparison on penetration rate due to individual diffusion mechanism shows that the concise correlation can be used to estimate the penetration of aerosols lesser than 0.2?m in diameter.The comparison between the previous experimental results and the theoretical estimations by using three coupling methods shows a big difference for aerosols from 0.1 to 1?m,and the difference increases with increasing crack length,decreasing crack height and decreasing pressure drop.The penetration rates estimated by the root square method are better than those by the coupling methods of product and addition.Only the strict theoretical solution can be used to effectively estimate the aerosol penetration when the crack height is very low,e.g.lower than 0.14 mm.For the case of rough inner surface,the estimated values by the method proposed in this study are in good agreement with the experimental values except for the ultrafine particles.As to monodispersed particles,the penetration factor increases with the increase of pressure difference and crack height,and the decrease of the crack length.Particles from 0.1?m to 1?m in diameters are less affected by various factors and maintain a higher penetration.For various cracks with 90? bends that are common in practice,such as L-shaped or Z-shaped,a simple model is proposed for calculating the aerosol penetration rate.Using the concise correlation obtained in this study to calculate the aerosol penetration rate due to pure diffusion through the whole crack,and the simple formula to obtain the penetration factor due to individual gravity through the horizontal part of the crack,then the square root coupling method is used to calculate the total penetration rate of the particles through the multi-bended cracks.Based on the analytical results for combined consideration of the diffusion and gravity obtained in an inclined channel,it can be confirmed by comparison that the gravity field cannot be accounted for the deposition of PM2.5 in the vertical channel.The effect of inertial impact on aerosol deposition can be neglected by analyzing the Stokes number in the multi-bended cracks.The penetration estimated by using the simple model proposed in this study agrees well with the experimental measurements when the crack height and the pressure difference are not too small.Only when the crack height is large,the influence of the number of bends on the particle penetration rate becomes obvious,and the particle penetration rate is positively correlated with the pressure difference and the crack height,and negatively correlated with the number of bends.Due to the dilute and capillary effects that may occur in practical problems,the gas flow can also be regarded as plug flow.The analytical solutions for particle concentration,deposition velocity and the penetration rate are obtained by theoretical solving the convective-diffusive equation in the plug flow regime.The results show that the particle concentration profile in building cracks in the plug and Poiseuille airflow regimes are significantly different.The particle deposition velocity on the lower wall decreases with the increasing dimensionless distance non-monotonically.Meanwhile,the difference between the deposition velocities of the aerosol particles on the upper and lower walls increased significantly with the increase of the deposition parameter,and the particle deposition velocity for the case of plug flow is significantly higher than that for Poiseuille flow.The estimated particle penetration rate under the condition of plug flow is lower than that of Poiseuille flow for all particles.In addition,the difference between the penetration rates under the two airflow patterns decreases firstly and then increases with the increase of particle size.The difference between the model predictions of plug and Poiseuille flow on the coarse particles is small.The crack roughness can strengthen the particle deposition and reduce the particle penetration for the two airflow patterns.For cracks with shorter length and higher height,and in the condition of larger pressure drop,the particle penetrations predicted in the plug flow are more exact than those in the Poiseuille airflow in a larger range of particle size.