Study on the Influence of Air Tightness of the Building Envelope on Indoor

sustainability

Article Study on the Inﬂuence of Air Tightness of the Building Envelope on Indoor Particle Concentration

Liang Yu 1,*, Ning Kang 1, Weikuan Wang 2, Huiyu Guo 1 and Jia Ji 3

1 School of Municipal and Environmental Engineering, Shenyang Jianzhu University, Shenyang 110168, China; [email protected] (N.K.); [email protected] (H.G.) 2 Shenyang Academy of Environmental Sciences, Shenyang 110179, China; [email protected] 3 Zhejiang Shilang Longshan Engineering Design Co. LTD, Zhejiang 310000, China; [email protected] * Correspondence: [email protected]

Received: 9 January 2020; Accepted: 22 February 2020; Published: 25 February 2020

Abstract: In order to grasp the building palisade structure tightness of indoor particulate matter mass concentration based on the particle penetration mechanism and settlement characteristics, this article analyzes the measurements of two different types of building air tightness of a Shenyang university office building in terms of indoor and outdoor particulate matter mass concentration levels from 2016-1-09 to 1-22, 2016-7-18 to 8-03, and 2017-2-28 to 3-13. The building outside the closed window that had no indoor source condition, the indoor office building and outdoor particle mass concentration, and the aperture size and shape of the envelope were analyzed to carry on the numerical simulation research by Fluent software, which was then analyzed; the results reveal that the measuring point of the I/O ratio is less than point B of the I/O ratio, measurement points of A linear regression fitting degree is lower than the fit of the measuring point B, and the causes for the measuring point A tightness (level 8) is superior to the measuring point B (level 4). When the gap height h is greater than 0.5 mm, the penetration rate of particles within the range of 0.25–2.5 µm particle size is close to 1. In different gap depths, the penetration rate of particles within the range of 0.1–1 µm particle size was close to 1. In diverse pressure difference, the 0.25–2.5 µm particles within the scope of penetration rate P is close to 1, the gap on both sides of the differential value ∆P; the greater the particle, the higher penetration rate. The larger the right-angle number of gap n, the lower the penetration rate of particles. The L-shaped gap and U-shaped gap have significantly better barrier effects in larger and smaller particles than the rectangular gap. The research results in this paper can help people understand and effectively control the influence of outdoor particles on the indoor air quality and provide reference data for the prediction of indoor particle mass concentration in buildings, which has theoretical basis and practical significance.

Keywords: atmospheric particulate matter pollutant; oﬃce buildings; air tightness of building envelope; indoor air quality; ﬂuent

1. Introduction In recent years, haze has occurred frequently in most areas of China, and outdoor air pollution has become serious. From the statistics of PM2.5 and PM10 on the pollution in the 2015–2017 Bulletin of the State of the environment of China [1] and the 2015–2017 Bulletin of the State of the environment of Shenyang [2], it was observed that the annual average of the PM2.5 mass concentration in China 3 3 and Shenyang decreased from 72 to 51 µg/ m and 50 to 43 µg/m and the average of the PM10 mass concentration decreased from 115 to 88 µg/m3 and 87 to 75 µg/m3. Although the pollution situation of the outdoor atmospheric particulate matter in China and Shenyang has been improved to some extent, it is still about 1.2 times higher than the current national standard for “Ambient air quality standards”

Sustainability 2020, 12, 1708; doi:10.3390/su12051708 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 1708 2 of 20

GB3095-2012 [3], and the pollution level of PM2.5 and PM10 in Shenyang is significantly higher than the national average. Relevant research shows that the increase in human mortality and morbidity has a significant relationship with human exposure to particulate matter [4]. The increasing incidence of lung and cardiovascular diseases is linked to increased concentrations of particulate matter, every 10% increase in the concentration of PM2.5 in the air, leading to an increase in lung function by about 1% and increase in the incidence of various respiratory illnesses by about 10% [5]. In modern societies, urban residents spend more than 90% of their time indoors. Therefore, people pay more and more attention to indoor air quality [6]. Indoor particulate matter pollution is more harmful to human health than outdoor particulate matter pollution. The particulate matter in indoor air has become one of the important factors affecting indoor air quality and indoor health. In modern office buildings, outdoor pollution sources rather than indoor sources are the main factors affecting indoor particulate pollution [7]. The study found that when there was no significant indoor particulate pollution source, 60–70% of the indoor PM2.5 mass density came from the outdoor particulate pollution [8]. When there were indoor pollution sources, 55–60% of the indoor PM2.5 mass concentration came from outdoor particulate pollution. The study showed that the monthly mean values of the indoor and outdoor PM2.5 mass concentration at the measurement points in summer were 104.1 and 49.2 µg/m3, respectively, which were lower than the winter mass concentration of 230.1 3 and 134.2 µg/m , and the I/O ratio of indoor PM2.5 in summer was also significantly lower than the winter value [9]. The study found that the indoor PM2.5/ PM10 ratio was higher than the outdoor PM2.5/ PM10 ratio, the indoor PM2.5 concentration was higher than the outdoor concentration, and the indoor PM2.5 concentration was higher than the outdoor concentration. The indoor particulate pollutants were mainly PM2.5 [10]. The study found mild haze weather in summer, and the weekly 3 average mass concentration of PM2.5 in buildings was 135.1 µg/m ; and in the moderate haze weather 3 in winter, the weekly mean mass concentration of PM2.5 in buildings was 231.6 µg/m [11]. This paper selected Shenyang, a typical city in a severely cold region, as the research object. As public buildings are the main gathering place of urban residents, many people were involved, it was easy for pathogens to gather, and the cross-infection rate was high. Therefore, it was necessary to study the indoor air pollution in public buildings. Therefore, the measurement point A (in the air tightness grade 8 green buildings) and point B (in the air tightness level 4 non-green building) of the two office buildings with different airtightness were selected from a university in Shenyang for actual measurement, according to the measured building palisade structure gap type; the calculation model was set up through a mathematical statistical analysis method where the fluent software numerical simulation method was used for particulate matter under the conditions of different influence factors to simulate the penetration coefficient changes with the particle size. The analysis of the influence of factors such as the gap geometry, size, and the pressure difference of indoor and outdoor on penetration coefficient were also conducted. It provided regional basic data for setting the PM2.5 limits of indoor air standards in China, provides a reference basis for the study of outdoor particulate barrier performance of buildings with different air tightness levels and the improvement of indoor environmental quality of buildings, and provides relevant research results for ensuring human health.

2. Materials and Method

2.1. Sampling Sites In this paper, two office buildings with different air tightness located in the campus of a university in Shenyang city were selected as the measured objects, and three measured points were implemented, namely, the measured points A and B (indoor) and C (outdoor), respectively. These are shown in Figure1, the measured situation is shown in Table1. Measuring point A is located in the meeting room (1st floor) within the main facade facing north, and the building structure is a frame structure with an area of 45 m2. Measuring point B is located in the equipment room (2nd floor) facing south of the main Sustainability 2020, 12, 1708 3 of 20 facade. The building structure is a brick-concrete structure with a building area of 50 m2. Survey of points A and B are shown in Table2.

Figure 1. Survey of points A, B, and C.

Table 1. Survey overview.

Measured Year Measured Time Number of Days Measured Content

In the winter of 2016 2016-1-09 to 2016-1-22 14 days Average daily concentration of PM2.5 and PM10 In the summer of 2016 2016-7-18 to 2016-8-03 17 days Average daily concentration of PM2.5 and PM10 In the winter of 2017 2017-2-28 to 2017-3-13 14 days Average daily concentration of PM2.5 and PM10

Table 2. Survey of exterior windows of observation points [12].

General Situation of the Content Point A Point B Outside the window towards North South Three layers of low-e glass Outside the window structure Plastic steel double glazing medium ﬁlled with argon External window installation method External type Nested External window opening mode Casement window Sliding window External window heat transfer coeﬃcient 0.93 2.70 (W/m2, K) Air tightness rating 8 4 Window width (mm) 5250 1000 Window height (mm) 3900 900 The number of windows in the building 2 3

2.2. Sampling Methods and Instruments During the measurement period, there was no obvious pollutant source in the measuring point, and during the test period, there was no personnel activity in the measuring point and the external windows and ventilation equipment were closed. Therefore, it can be approximately considered that there was no obvious particle source at the measuring points A and B. The measuring points were arranged in accordance with the national standards for “Indoor air quality” GB/T18883-2002 [13]. The detection method followed the industry standard for “Technical requirement and test procedures for total suspended particulates sampler” HJ/T374-2007 [14], “Total Suspended Particulates Sampler” JJG 943-2011 [15], “Determination of atmospheric articles PM10 and PM2.5 inin ambient air by gravimetric method” HJ618-2011 [16], “Specification and Test procedures for (PM10 and PM2.5) sampler” HJ93-2013 [17] and the European Union standards for “atmospheric total Sustainability 2020, 12, 1708 4 of 20 suspended particle sampler” regulation. The dailyily averageaverage massmass concentrationconcentration ofof indoorindoor andand outdoor particulate matter in office buildings was measured using the gravimetric method. The omeasurementﬃce buildings instruments was measured used using were the the gravimetric Lao ying method. 20302030 intelligentintelligent The measurement TSPTSP samplersampler instruments andand thethe used COMDECOMDE were theDERENDA Lao ying particles 2030 intelligent sampler, TSP instrument sampler andappearance the COMDE (Figure(Figure DERENDA 22 andand FigureFigure particles 3),3), instrumentinstrument sampler, instrument measuringmeasuring appearancerange and accuracy (Figures (Tables2 and3), 3 instrument and 4). measuring range and accuracy (Tables3 and4).

Figure 2. Lao ying 2030 TSP sampler.

Figure 3. COMDE DERENDA particulate sampler. Table 3. Lao ying 2030 TSP sampler technical parameters.

Technical Parameters The Parameter Value Sampling rate 100 L/min Flow accuracy 5.0% or less ± Sampling time Set anything within 100 h Timing accuracy Less than 1 s within 20 min ± Inlet velocity of sampling head 0.3 m/s PM sampling head diameter D = (2.5 0.2) µm 2.5 ± PM sampling head diameter D = (10 0.5) µm 10 ± A membrane diameter Φ 80 mm Applicable to ambient temperature range 20–40 C − ◦ Applicable to ambient humidity range 0–95% rH Sustainability 2020, 12, 1708 5 of 20

Table 4. COMDE DERENDA sampler technical parameters.

Technical Parameters The Parameter Value Sampling flow range 1.5–3.5m/h (adjustable)3 Rated flow 2.3 m/h3 Flow accuracy The deviation within 24 h is less than 2% Load capacity The flow is 2.3m/h, the resistance should not be less than 45kpa3 Sampling time 1 min to 999 h (adjustable) Timing accuracy Less than 1s within 20 min ± Effective filter diameter 47–50 mm Applicable to ambient temperature range 30–50 C − ◦ Applicable to ambient humidity range 0–100% rH

3. Processing of Measured Data

3.1. I/O Ratio

For the average of PM2.5 and PM10 mass concentration I/O ratios taken in winter 2016, the measurement points for A were 0.60 and 0.48 and for B were 0.67 and 0.53; in summer 2016, the measurement points for A were 0.34 and 0.30 and for B were 0.40 and 0.32; in winter 2017, the measurement points for A were 0.38 and 0.33 and for B were 0.44 and 0.36. The I/O ratio of PM2.5 and PM10 varies over time (Figure4). By comparing the I/O values of PM2.5 and PM10 measured three times, we found that the average of I/O in the winter of 2015 > winter of 2016 > summer of 2015; at the same time, the I/O ratio of the PM2.5 and PM10 varied with time in a consistent manner, but the mean of I/O ratio of measurement point A is less than the mean of measurement point B, and the change trend of I/O ratio of measurement point A is relatively ﬂat. Considering that the air tightness of the building envelope at measurement point A is better than that at measurement point B, it can delay the inﬂuence of outdoor particles indoors in a better manner.

3.2. Linear Regression

The regression analysis of the average daily mass concentration of indoor and outdoor PM2.5 measured three times in winter 2016, summer 2016, and winter 2017 shows that the linear regression 2 fitting R of indoor and outdoor PM2.5 mass concentration in point A reached 0.8346, 0.3747, and 2 0.8348, while the linear regression fitting R of indoor and outdoor PM2.5 mass concentration in point B reached 0.8411, 0.6077, and 0.8231. The linear regression fitting R2 of indoor and outdoor PM10 mass concentration at point A reached 0.8889, 0.4062, and 0.8583. The linear regression fitting R2 of indoor and outdoor PM10 mass concentration at point B reached 0.8741, 0.6563, and 0.9074. The average daily mass concentration curve fitting is shown in Figure5. When the doors and windows were closed and there was no obvious pollution source in the room, the average daily mass density of the indoor and outdoor particles in the three types of measurement became highly correlated. Winter 2015 R2 > winter 2016 R2 > summer 2016 R2; at the same time, R2 of B >R2 of A. This is because the containment structure of point A has good air tightness, which weakens the correlation between the concentration of indoor and outdoor particles. Sustainability 2020, 12, 1708 6 of 20 Sustainability 2020, 12, 1708 6 of 21

(a)

(b) Figure 4. Cont. Sustainability 2020, 12, 1708 7 of 20 Sustainability 2020, 12, 1708 7 of 21

(c)

Figure 4.FigureDaily 4. changes Daily changes of PM of PMand2.5 and PM PMI10/O I/O ratios. ratios. (a) In In the the winter winter of of2016, 2016, (b) In (b )the In summer the summer of of Sustainability 2020, 12, 1708 2.5 10 8 of 21 2016, (c) In2016, the (c winter) In the winter of 2017. of 2017.

By comparing the I/O values of PM2.5 and PM10 measured three times, we found that the average of I/O in the winter of 2015 > winter of 2016 > summer of 2015; at the same time, the I/O ratio of the PM2.5 and PM10 varied with time in a consistent manner, but the mean of I/O ratio of measurement point A is less than the mean of measurement point B, and the change trend of I/O ratio of measurement point A is relatively flat. Considering that the air tightness of the building envelope at measurement point A is better than that at measurement point B, it can delay the influence of outdoor particles indoors in a better manner.

3.2. Linear Regression

(a)

Figure 5. Cont. SustainabilitySustainability2020, 12, 17082020, 12, 1708 9 of 21 8 of 20

(b)

(c)

Figure 5. Linear regression analysis of indoor and outdoor PM2.5 and PM10 concentration. (a) In the Figure 5. Linear regression analysis of indoor and outdoor PM2.5 and PM10 concentration. (a) In the winter ofwinter 2016, of (b 2016,) In the (b) summerIn the summer of 2016, of 2016, (c) ( Inc) In the the winter winter ofof 2017.2017.

4. Numerical Simulation Results According to the abovementioned results and data analysis, the mass concentration of the indoor particulate matter in office buildings with no indoor air conditioning and ventilation equipment and no significant particulate matter pollution sources is mainly affected by the pollution degree of the outdoor particulate matter. The air tightness of the building envelope is one of the key factors that determine the outdoor particulate matter entering indoors through permeation ventilation [18–22]. There are Sustainability 2020, 12, 1708 10 of 21 Sustainability 2020, 12, 1708 10 of 21 When the doors and windows were closed and there was no obvious pollution source in the room,When the average the doors daily and mass windows density were of closedthe indoor and thereand outdoorwas no obviousparticles pollution in the three source types in theof measurementroom, the average became daily highly mass correlated. density ofWinter the indoor 2015 R and2 > winter outdoor 2016 particles R2 > summer in the 2016three R types2; at the of samemeasurement time, R2 becameof B >R 2highly of A. correlated.This is because Winter the 2015 containment R2 > winter structure 2016 R2 >of summer point A 2016 has Rgood2; at airthe tightness,same time, which R2 of weakens B >R2 of the A. correla This tionis because between the the containment concentration structure of indoor of andpoint outdoor A has particles.good air tightness, which weakens the correlation between the concentration of indoor and outdoor particles. 4. Numerical Simulation Results 4. Numerical Simulation Results According to the abovementioned results and data analysis, the mass concentration of the indoorAccording particulate to thematter abovementioned in office buildings results withand nodata indoor analysis, air theconditioning mass concentration and ventilation of the equipmentindoor particulate and no significant matter in particulate office buildings matter pollutionwith no sourcesindoor isair mainly conditioning affected byand the ventilation pollution degreeequipment of the and outdoor no significant particulate particulate matter. Thematter air pollutiontightness sourcesof the building is mainly envelope affected is by one the of pollution the key factorsdegreeSustainability ofthat the2020 determineoutdoor, 12, 1708 particulate the outdoor matter. particulat The air etigh mattertness ofentering the building indoors envelope through is one permeation of the9 key of 20 ventilationfactors that [18–22]. determine There the are outdoormany kinds particulat of gapse inmatter the envelopeentering structure.indoors Forthrough office permeation buildings, theyventilationmany are kinds mainly [18–22]. of gaps around inThere the the envelopeare external many structure. kindswindow of For gapsbetween offi ince the buildings,the envelope window they structure.pane are mainly and Forthe around officewindow thebuildings, externalframe, betweentheywindow are the betweenmainly window around the frame window the and external pane the andwall, window the electrical window between entrance, frame, the between windowexterior the wallpane window gap, and and the frame thewindow andgap thearound frame, wall, thebetweenelectrical door frame;the entrance, window these exterior areframe mainly wall and gap, thedetermined wall, and the electrical gap by aroundthe entrance, gap thesize door exteriorand frame;geometric wall these gap, shape are and mainly of the the gap determined envelope around structuretheby thedoor gap frame;[23]. size Therefore, these and geometricare mainlyin order shape determined to study of the the envelopeby threlationshipe gap structure size andbetween [ 23geometric]. Therefore,the mass shape concentration in of order the envelope to study of indoorstructurethe relationship and [23]. outdoor Therefore, between particulate thein order mass matter concentrationto in study office the buildings ofrelationship indoor and and the between outdoorgap size the particulateand mass shape concentration of matter the building in offi ofce envelope,indoorbuildings and andnumerical outdoor the gap particulate simulation size and shape matter was of inconducted the office building buildings in envelope, this and paper numericalthe gapconcerning size simulation and theshape gap was of conductedtheof externalbuilding in windowsenvelope,this paper with numerical concerning different simulation the sizes gap and of externalshapeswas conducted under windows di fferentin with this indoor dipaperfferent and concerning sizes outdoor and shapes pressurethe gap under differences.of diexternalfferent Generally,windowsindoor and withthere outdoor different are three pressure sizes types and di ffof erences.shapes gaps underin Generally, the dienvelope:fferent there indoor square are three and-shape typesoutdoor gap, of gapspressureL-shaped in the differences. gap, envelope: and U-shapedGenerally,square-shape gap there gap,(Figure are L-shaped three6). In typesthe gap, three-dimensional andof gaps U-shaped in the gap envelope:di (Figureagram,6 the).square In gap the-shape length three-dimensional gap,is represented L-shaped diagram, bygap, W, andthe the gapU-shapedgap height length gapby is h, represented (Figure and the 6). gap In by thedepth W, three-dimensional the by gap d. heightThe three-dimensional by h,diagram, and the the gap structuregap depth length by is d.shownis Therepresented three-dimensional in Figure by 7. W, the gapstructure height is by shown h, and in the Figure gap7 depth. by d. The three-dimensional structure is shown in Figure 7.

Figure 6. Envelope structure gap schematic diagram. Figure 6. Envelope structure gap schematic diagram. Figure 6. Envelope structure gap schematic diagram.

Figure 7. Rectangular gap 3D illustration. Figure 7. Rectangular gap 3D illustration. 4.1. Principle of Calculation ModelFigure 7. Rectangular gap 3D illustration. 4.1. Principle of Calculation Model 4.1. PrincipleIn this paper,of Calculation the discrete Model phase model was used for simulation. Whether the flow pattern is turbulentIn this or paper, laminar the depends discrete on phase whether model the was Reynolds used for number simulation. exceeds Whether the critical the Reynolds flow pattern number. is turbulentThe ReynoldsIn this or paper, laminar number the depends ofdiscrete all the phaseon flow whether problems model thewas involved Re usynoldsed for in thissimulation.number paper exceeds is lessWhether than the 2320, thecritical flow so it Reynoldspattern is laminar is number.turbulentsteady flow The or and Reynoldslaminar the pressure dependsnumber gradient ofon all whether the is flow zero. theproblems During Reynolds the involved penetration number in this exceeds of paper particulate isthe less critical matter than 2320, inReynolds the so gap it isnumber.of laminar the envelope The steady Reynolds structure, flow and number thethe pressure,pressure of all the density,gradient flow problems and is zero. temperature Duringinvolved the distribution in penetration this paper of the isof less particulate gap than facing 2320, thematter so flow it inisfield thelaminar havegap ofsteady little the e ffenvelope flowect, andand asstructure,the the pressure gap the depth gradient pressure d is short, is, density,zero. it canDuring and be approximated temperaturethe penetration distribution that of the particulate air temperature of the matter gap facinginat the the gap flow inletof the field and envelope have outlet littledoes structure, effect, not change. andthe aspressure Therefore,the gap, density, depth in the d andis process short, temperature ofit can particulate be approximateddistribution matterpenetrating of thatthe gapthe airfacingthe temperature gap the of flow the envelope fieldat the have gap structure, little inlet effect, and the outlet and effects as does the of thegapnot thermophores change.depth d Therefore,is short, and it pressure canin the be approximatedprocess gradient of forceparticulate that on the the matterairmotion temperature penetrating of the particulate at the gap matter inletof the and canenvelope outlet be ignored, doesstructur no i.e.,te, change. itthe is mainlyeffects Therefore, of aff theected thermophoresin bythe the process combined andof particulate pressure effects of mattergravity, penetrating Brownian force,the gap and of dragthe envelope force. The structur sum ofe, thethe forceseffects exerted of the thermophores on the particles and is shownpressure in Table5. The pre-processing software gambit was used for modeling and meshing. Considering the regular structure of the gap, a quadrilateral mesh was selected. The whole model was divided into about 300,000 element meshes. The meshing is shown in Figure8.

Table 5. Particulate matter the force magnitude.

Force The Force of Gravity Drag Force Brown Force Pressure Gradient Force Thermophores Force 15 14 15 17 Orders of magnitude 10− 10− 10− 0 10− Sustainability 2020, 12, 1708 11 of 21 gradient force on the motion of the particulate matter can be ignored, i.e., it is mainly affected by the combined effects of gravity, Brownian force, and drag force. The sum of the forces exerted on the particles is shown in Table 5. The pre-processing software gambit was used for modeling and Sustainabilitymeshing. Considering2020, 12, 1708 the regular structure of the gap, a quadrilateral mesh was selected. The whole10 of 20 model was divided into about 300,000 element meshes. The meshing is shown in Figure 8.

(a)

(b)

Figure 8. Meshing. ( a)) 2D 2D Meshing Meshing and ( b) 3D Meshing. 4.2. Setting of Boundary Conditions and Basic Parameters Table 5. Particulate matter the force magnitude. The particle size range of the particles studied in this paper was 0.001–100 µm, and it was assumed The Force of Pressure Gradient Thermophores Force Drag Force Brown Force that the particles were coalGravity ash. The Rosin–Rammler distribution was used forForce particle size distribution.Force OrdersThe following of assumptions were made in the simulation: 10−15 10−14 10−15 0 10−17 magnitude (1) becauseSustainability the 2020 volume, 12, 1708 fraction of particulate matter in the atmosphere is very small, its subsidence12 of 21 had little effect on the laminar flow, and the effect of particulate matter on laminar flow was 4.2. Settingdifferential of Boundary pressure Conditions is less andthan Basic 10 pa. Parameters In this paper, the air density = 1.342 kg/m³ at the average ignored (Table6); outdoor temperature of −10℃ in January in Shenyang was selected, and the coefficient of dynamic (2) Theonly particle the influence size range of gravity, of the Brownian particles force, studied and in drag this force paper on was particles 0.001–100 were considered;μm, and it was viscosity was 1.67 × 10−5 pa∙s. (3)assumedthe airthat passing the particles through were the coal gap ash. was incompressibleThe Rosin–Rammler and met distribution the Bussinesq was used approximation; for particle size distribution.According to the ASHRAE manual, the gap height of the envelope is generally between 0.05 (4) the heat transfer between the air and particulate matter was ignored; Theand following 3 mm. At assumptions this time, the were flow made state in of the the simulation: permeation ventilation in the gap of the envelope is (5) thelaminar particles flow. were The spherical size of the smooth average particles air velocity (spherical); u only depends on the gap height h, gap depth d, (6)1) becausetheand particles the the pressure volume were notdifference fraction charged of between andparticulate there the was matter two no electrostatic sidein thes ofatmosphere the friction, gap butis condensation,very has small, nothing its collision, subsidenceto do with or the hadchemicalstructure little reaction effectof the on gap among the [24]. laminar them, When andflow, the the seam and particle thelength ef sizefect is did Wof not =particulate 0.5 change m, d = during matte3 cm, rtheand on penetration laminarthe various flow process; parameters was (7) ignoredthewhen particles the (Table air werepasses 6); inert through particles. the gap of the envelope are shown in Table 6. 2) only the influence of gravity, Brownian force, and drag force on particles were considered; 3) the air passing throughTable the 6.TableAirflow gap 6. was Airflow parameters incompre parameters (Wssible= 0.5 (W and m, = 0.5 d met= m,0.03 thed = m, 0.03Bussinesq n = m,0). n = 0).approximation; 4) the heat transfer between the air and particulate matter was ignored; Differential Pressure on Mean Velocity of Air in the Gap u 5) theGap particles Height h were (mm) spherical Differential smooth Pressure particles on (spherical);Mean Velocity of Air in Reynolds Number Re Gap Height h (mm) Both Sides (pa)ΔP (m/s) Reynolds Number Re 6) the particles were not chargedBoth Sides and (pa) there was no electrostaticthe Gap u (mfriction,/s) condensation, collision, or 1 5 0.7370 118.09 chemical1 reaction among them, 5and the particle size 0.7370did not change during the 118.09 penetration 1 7 0.9940 159.28 process;1 7 0.9940 159.28 11 1010 1.3510 1.3510 216.48 216.48 7) the particles were inert particles. 0.50.5 55 0.2050 0.2050 16.45 16.45 0.5 7 0.2860 22.95 Under the0.5 action of inside and outside7 differential pressure 0.2860 ΔP, the airflow enters the indoor 22.95 0.5 10 0.4070 32.66 through a structure0.10.5 crack. The pressure10 5 difference is caused 0.0082 by indoor 0.4070 and outdoor 0.132wind pressure 32.66 and thermodynamic0.10.1 pressure; additionally, 75 the building palisade 0.0144 0.0082 structure on both 0.231 sides 0.132of the 0.10.1 107 0.0163 0.0144 0.262 0.231 0.1 10 0.0163 0.262 Under the action of inside and outside differential pressure ∆P, the airflow enters the indoor through a structureThe boundary crack. conditions The pressure of this diff erencesimulation is caused are defined by indoor as follows: and outdoor wind pressure and 1) inlet: the continuous phase air is set as “velocity-inlet” and the discrete phase particle is set as “escape”; 2) solid wall: the continuous phase air boundary condition is “no slip (fixed boundary)” and the discrete phase particle boundary condition is “trap”; 3) export (outlet): continuous phase boundary condition is set as free air flow (outflow) and the discrete phase particles are set as “escape” (escape). As observed from the above table, the airflow flow pattern wherein air penetrates into the room through the gap of the envelope structure is generally laminar flow, and the air velocity in the gap only depends on the gap shape, gap size, and the pressure difference between the two sides of the gap. In this paper, the Fluent software was used to simulate the penetration of particles with particle size between 0.001 and 100 μm. –The particles with particle size between 0.001 and 100 μm were divided into 10 particle size segments: 0.001–0.005 μm, 0.005–0.01 μm，0.01–0.05 μm, 0.05–0.1 μm, 0.1–0.5 μm, 0.5–1 μm, 1–2.5 μm, 2.5–10 μm, 10–50 μm, 50–100 μm. Assuming that the number of particles at the entrance of each particle size segment is 200, the ratio of the number of particles at the exit of each particle size segment divided by the number of particles at the entrance is the penetration coefficient, represented by P and the formula is as follows: 𝑁 𝑃 𝑁 (1)

N escape—the number of escaping particles at the exit; N inlet—number of particles at the inlet. Sustainability 2020, 12, 1708 11 of 20 thermodynamic pressure; additionally, the building palisade structure on both sides of the differential pressure is less than 10 pa. In this paper, the air density = 1.342 kg/m3 at the average outdoor temperature of 10°C in January in Shenyang was selected, and the coefficient of dynamic viscosity − was 1.67 10 5 pa s. × − · According to the ASHRAE manual, the gap height of the envelope is generally between 0.05 and 3 mm. At this time, the flow state of the permeation ventilation in the gap of the envelope is laminar flow. The size of the average air velocity u only depends on the gap height h, gap depth d, and the pressure difference between the two sides of the gap but has nothing to do with the structure of the gap [24]. When the seam length is W = 0.5 m, d = 3 cm, and the various parameters when the air passes through the gap of the envelope are shown in Table6. The boundary conditions of this simulation are defined as follows:

(1) inlet: the continuous phase air is set as “velocity-inlet” and the discrete phase particle is set as “escape”; (2) solid wall: the continuous phase air boundary condition is “no slip (fixed boundary)” and the discrete phase particle boundary condition is “trap”; (3) export (outlet): continuous phase boundary condition is set as free air flow (outflow) and the discrete phase particles are set as “escape” (escape).

As observed from the above table, the airflow flow pattern wherein air penetrates into the room through the gap of the envelope structure is generally laminar flow, and the air velocity in the gap only depends on the gap shape, gap size, and the pressure difference between the two sides of the gap. In this paper, the Fluent software was used to simulate the penetration of particles with particle size between 0.001 and 100 µm. –The particles with particle size between 0.001 and 100 µm were divided into 10 particle size segments: 0.001–0.005 µm, 0.005–0.01 µm, 0.01–0.05 µm, 0.05–0.1 µm, 0.1–0.5 µm, 0.5–1 µm, 1–2.5 µm, 2.5–10 µm, 10–50 µm, 50–100 µm. Assuming that the number of particles at the entrance of each particle size segment is 200, the ratio of the number of particles at the exit of each particle size segment divided by the number of particles at the entrance is the penetration coefficient, represented by P and the formula is as follows:

Nescape P = (1) Ninlet

N escape—the number of escaping particles at the exit; N inlet—number of particles at the inlet.

4.3. Simulation Results

4.3.1. Influence of Gap Height on Penetration Coefficient When retaining structure gap on both sides of the differential ∆P = 10 pa, the air inlet temperature is 263 k, d = 0.03 m, W = 0.5 m in length as the conditions; and at the same time, only consider the effect of different gap heights h on the penetration rate of particles The variation of the penetration coefficient P with particle size at three gap heights (1, 0.5, and 0.1 mm) was simulated. Under h = 0.5 mm, the velocity vector and pressure vector of the airflow are shown in Figures9–11, respectively. Under different gap heights, the law of penetration changed with different particle sizes (Figure 12). In Figure 12, among all particles with particle sizes, the particles with particle sizes between 0.25 and 0.75 µm has the highest penetration rate. Particle size is less than 0.25 µm, the penetration rate P increased with the increase of particle size, particle size is greater than 0.25 microns, the penetration rate P decreases with the increase of particle size, and all this is because the smaller particle size of particles was mainly affected by brown diffusion, and the particle size of larger particles, mainly the gravity effect, under the action of these two kinds of force is bigger; smaller particles are easily captured by the wall of the retaining envelope structure and deposited on its surface. When h = 1 mm, the Sustainability 2020, 12, 1708 13 of 21 Sustainability 2020, 12, 1708 13 of 21 Sustainability 2020, 12, 1708 13 of 21

4.3. Simulation Results 4.3. Simulation Results 4.3. Simulation Results 4.3.1. Influence of Gap Height on Penetration Coefficient 4.3.1. Influence of Gap Height on Penetration Coefficient 4.3.1. Influence of Gap Height on Penetration Coefficient When retaining structure gap on both sides of the differential ΔP = 10 pa, the air inlet When retaining structure gap on both sides of the differential ΔP = 10 pa, the air inlet temperatureWhen retaining is 263 structure k, d = 0.03 gap m, Won =both 0.5 m sides in length of the as differentialthe conditions; ΔP and= 10 at pa, the thesame air time, inlet only Sustainabilitytemperature2020 ,is12 263, 1708 k, d = 0.03 m, W = 0.5 m in length as the conditions; and at the same time,12 of only 20 temperatureconsider theis 263 effect k, d of = different0.03 m, W ga =p 0.5heights m in h length on the as penetration the conditions; rate of and particles at the Thesame variation time, only of the consider the effect of different gap heights h on the penetration rate of particles The variation of the considerpenetration the effect coefficient of different P with gap particle heights sizeh on at the three penetration gap heights rate (1, of 0.5,particles and 0.1 The mm) variation was simulated. of the penetration coefficient P with particle size at three gap heights (1, 0.5, and 0.1 mm) was simulated. penetrationpenetrationUnder h ratecoefficient= 0.5 of mm, particles theP with velocity with particle particle vector size size and at rangingthree pressure gap from vectorheights 0.01 of to (1, the 10 0.5,µ airflowm and exceeded 0.1 are mm) shown 95%. was Whenin simulated. Figures h = 0.5 9–11, Under h = 0.5 mm, the velocity vector and pressure vector of the airflow are shown in Figures 9–11, Undermm,respectively. the h = penetration 0.5 mm, Under the rate velocity different of particles vector gap within andheights, pressure the rangethe lawvector of 0.25–2.5of ofpenetration theµ mairflow exceeded changed are shown 90%. with When in differentFigures h = 0.1 9–11, particle mm, respectively. Under different gap heights, the law of penetration changed with different particle respectively.thesizes penetration (Figure Under rate 12). isdifferent the highest gap when heights, the particlethe law sizeof penetration is around 0.4 changedµm, and with the penetrationdifferent particle rate of sizes (Figure 12). sizesthe particles (Figure is12). about 50%.

Figure 9. Inlet velocity vector (h = 0.5mm). Figure 9. Inlet velocity vector (h = 0.5mm). Figure 9. InletInlet velocity velocity vector vector (h (h == 0.5mm).0.5mm).

Figure 10. Outlet velocity vector (h = 0.5mm). FigureFigure 10. 10.Outlet Outlet velocity velocity vector vector (h (h= =0.5mm). 0.5mm). Figure 10. Outlet velocity vector (h = 0.5mm).

Sustainability 2020, 12, 1708 14 of 21 FigureFigure 11. Stress11. Stress vector vector diagram diagram (h = (h0.5 = mm).0.5 mm). Figure 11. Stress vector diagram (h = 0.5 mm). Figure 11. Stress vector diagram (h = 0.5 mm).

FigureFigure 12.12. PenetrationPenetration raterate betweenbetween thethe particleparticle sizesize ofof gapgap heightheight ((∆ΔP P= = 10 pa, dd = 3 cm)

In Figure 12, among all particles with particle sizes, the particles with particle sizes between 0.25 and 0.75 μm has the highest penetration rate. Particle size is less than 0.25 μm, the penetration rate P increased with the increase of particle size, particle size is greater than 0.25 microns, the penetration rate P decreases with the increase of particle size, and all this is because the smaller particle size of particles was mainly affected by brown diffusion, and the particle size of larger particles, mainly the gravity effect, under the action of these two kinds of force is bigger; smaller particles are easily captured by the wall of the retaining envelope structure and deposited on its surface. When h = 1 mm, the penetration rate of particles with particle size ranging from 0.01 to 10 μm exceeded 95%. When h = 0.5 mm, the penetration rate of particles within the range of 0.25–2.5 μm exceeded 90%. When h = 0.1 mm, the penetration rate is the highest when the particle size is around 0.4 μm, and the penetration rate of the particles is about 50%.

4.3.2. Influence of Gap Depth on Penetration Coefficient With the palisade structure gap on both sides of the differential ΔP = 10 pa, an air inlet temperature of 263 k, h = 1 mm, W = 0.5 m，only consider the effect of different gap depths d on the penetration rate of particles In this paper, the variation of penetration rate P was simulated with the particle size in different gap depths (70, 50, 30 mm). The flow parameters of the gaps in different depths are shown in Table 7. Under the conditions of d = 5 cm and d = 7 cm, the velocity vector and pressure vector of the airflow are as shown in Figures 13–18 respectively. In different gap depths, the variation law of penetration with different particle sizes is as shown in Figure 19.

Figure 13. Pressure vector (d = 5cm).

Figure 14. Pressure vector (d = 7cm). Sustainability 2020, 12, 1708 14 of 21 Sustainability 2020, 12, 1708 14 of 21

Figure 12. Penetration rate between the particle size of gap height (Δ P = 10 pa, d = 3 cm) Figure 12. Penetration rate between the particle size of gap height (Δ P = 10 pa, d = 3 cm) In Figure 12, among all particles with particle sizes, the particles with particle sizes between In Figure 12, among all particles with particle sizes, the particles with particle sizes between 0.25 and 0.75 μm has the highest penetration rate. Particle size is less than 0.25 μm, the penetration 0.25 and 0.75 μm has the highest penetration rate. Particle size is less than 0.25 μm, the penetration rate P increased with the increase of particle size, particle size is greater than 0.25 microns, the rate P increased with the increase of particle size, particle size is greater than 0.25 microns, the penetration rate P decreases with the increase of particle size, and all this is because the smaller Sustainabilitypenetration2020, rate12, 1708 P decreases with the increase of particle size, and all this is because the13 smaller of 20 particle size of particles was mainly affected by brown diffusion, and the particle size of larger particle size of particles was mainly affected by brown diffusion, and the particle size of larger particles, mainly the gravity effect, under the action of these two kinds of force is bigger; smaller particles, mainly the gravity effect, under the action of these two kinds of force is bigger; smaller 4.3.2.particles Influence are easily of Gap captured Depth by on Penetrationthe wall of Coethe ffiretainingcient envelope structure and deposited on its particles are easily captured by the wall of the retaining envelope structure and deposited on its surface. When h = 1 mm, the penetration rate of particles with particle size ranging from 0.01 to 10 surface.With the When palisade h = 1 structure mm, the gap penetration on both sides rate ofof theparticles differential with ∆particleP = 10 pa,size an ranging air inlet from temperature 0.01 to 10 μm exceeded 95%. When h = 0.5 mm, the penetration rate of particles within the range of 0.25–2.5 of 263μm k,exceeded h = 1 mm, 95%. W =When0.5 m, h only= 0.5 consider mm, the the penetration effect of di ffraerentte of gapparticles depths within d on the the penetration range of 0.25–2.5 rate μm exceeded 90%. When h = 0.1 mm, the penetration rate is the highest when the particle size is of particlesμm exceeded In this 90%. paper, When the h variation = 0.1 mm, of penetrationthe penetration rate raP tewas is simulatedthe highest with when the the particle particle size size in is around 0.4 μm, and the penetration rate of the particles is about 50%. diffarounderent gap 0.4 depths μm, and (70, the 50, penetration 30 mm). The rate flow of parametersthe particles of is the about gaps 50%. in di fferent depths are shown in Table7. Under the conditions of d = 5 cm and d = 7 cm, the velocity vector and pressure vector of 4.3.2. Influence of Gap Depth on Penetration Coefficient the4.3.2. airflow Influence are as shownof Gap inDepth Figures on Penetration 13–18 respectively. Coefficient In different gap depths, the variation law of penetrationWith the with palisade different structure particle sizesgap on is as both shown sides in Figureof the 19 differential. ΔP = 10 pa, an air inlet With the palisade structure gap on both sides of the differential ΔP = 10 pa, an air inlet temperature of 263 k, h = 1 mm, W = 0.5 m，only consider the effect of different gap depths d on the temperature of 263 k, h = 1 mm, W = 0.5 m，only consider the effect of different gap depths d on the penetration rate ofTable particles 7. Slot In flow this parameters paper, the at variation different depths of penetration (H = 1mm, rate∆P P= 10was pa). simulated with the penetration rate of particles In this paper, the variation of penetration rate P was simulated with the particle size in different gap depths (70, 50, 30 mm). The flow parameters of the gaps in different Gapparticle Depth size d (mm) in different Differential gap Pressure depths (pa) (70, Gap50, Height30 mm). h (mm) The flow Air Velocity parameters v (m/s) of Reynoldsthe gaps Number in different Re depths are shown in Table 7. Under the conditions of d = 5 cm and d = 7 cm, the velocity vector and depths30 are shown in Table 10 7. Under the conditions 1 of d = 5 cm and 1.351 d = 7 cm, the velocity 216.48 vector and pressure 50vector of the airflow 10 are as shown in Figures 1 13–18 respectively. 0.910 In different gap 146.01 depths, the pressure70 vector of the airflow 10 are as shown in Figu 1res 13–18 respectively. 0.677 In different 108.69gap depths, the variation law of penetration with different particle sizes is as shown in Figure 19. variation law of penetration with different particle sizes is as shown in Figure 19.

Figure 13. Pressure vector (d = 5cm). FigureFigure 13. 13.Pressure Pressure vector vector (d =(d5cm). = 5cm).

Sustainability 2020, 12, 1708 15 of 21 Figure 14. PressurePressure vector (d(d == 7cm). Figure 14. Pressure vector (d = 7cm).

Figure 15. InletInlet velocity velocity vector vector (d (d = 5cm).5cm).

Figure 16. Outlet velocity vector (d = 5cm).

Figure 17. Inlet velocity vector (d = 7cm).

Figure 18. Outlet velocity vector (d = 7cm). Sustainability 2020, 12, 1708 15 of 21 Sustainability 2020, 12, 1708 15 of 21 Sustainability 2020, 12, 1708 15 of 21

Figure 15. Inlet velocity vector (d = 5cm). Sustainability 2020, 12, 1708 Figure 15. Inlet velocity vector (d = 5cm). 14 of 20 Figure 15. Inlet velocity vector (d = 5cm).

Figure 16. Outlet velocity vector (d = 5cm). Figure 16. Outlet velocity vector (d = 5cm). FigureFigure 16. 16.Outlet Outlet velocity velocity vector vector (d (d= =5cm). 5cm).

Sustainability 2020, 12, 1708 16 of 21

Table 7. Slot flow parameters at different depths (H = 1mm, ΔP = 10 pa).

Differential Reynolds Number Gap Depth d (mm) Gap Height h (mm) Air Velocity v (m/s). Pressure (pa) Re Figure 17. Inlet velocity vector (d = 7cm). 30 10 FigureFigure 17. 17. InletInlet velocity velocity 1 vector vector (d (d == 7cm).7cm). 1.351 216.48 50 10 Figure 17. Inlet velocity 1 vector (d = 7cm). 0.910 146.01 70 10 1 0.677 108.69

In Figure 19 the penetration rate P decreases with an increase of gap depth d. In the range of 0.1–1μm, the penetration rate of particles at different gap depths was close to 1. When the particle size is less than 0.1μm, the penetration rate decreases with an increase of gap depth d, as the particles with smaller size are mainly affected by the Brownian diffusion. When the particle size is greater than 2.5 μm, the penetration rate decreases with an increase of gap depth d, as particles with larger particle sizes are mainly affected by a gravity settlement. The larger gap depth increases the residence time of particles in the gap of the envelope, thus increasing the probability of particles contacting the gap wall. Figure 18. Outlet velocity vector (d = 7cm). Figure 18. Outlet velocity vector (d = 7cm). Figure 18. Outlet velocity vector (d = 7cm). Figure 18. Outlet velocity vector (d = 7cm).

FigureFigure 19. Penetration 19. Penetration rate of rate each of eachparticle particle size sizesegment segment at different at diﬀerent gap gap depths depths (Δ (P∆ =P 10= pa,10pa, h =1 h =mm)1 mm).

In Figure 19 the penetration rate P decreases with an increase of gap depth d. In the range of 4.3.3. Influence of Pressure Difference between the two Sides of the Gap on the Penetration 0.1–1µm, the penetration rate of particles at different gap depths was close to 1. When the particle Coefficient size is less than 0.1µm, the penetration rate decreases with an increase of gap depth d, as the particles with smallerWhen the size air are inlet mainly temperature affected byis 263 the k, Brownian h = 1 mm, di ffWusion. = 0.5 m, When d = the30 mm, particle only size consider is greater the than gap 2.5on µbothm, the sides penetration of the differential. rate decreases ΔP does with not an increase influence of particle gap depth penetration d, as particles rate. with At the larger same particle time, the variation of penetration coefficient P caused by the change of particle size in diverse gap pressure difference (5, 7, 10 pa) was simulated in this paper. In ΔP = 5 pa, ΔP = 7 pa cases, the velocity vector and pressure vector of the airflow are as shown in Figures 20–23 respectively., when the pressure difference between the two sides of the gap changes, the change law of penetration rate has diverse particle sizes (Figure 24).

Figure 20. Velocity vector (Δ P = 5 pa). Sustainability 2020, 12, 1708 16 of 21

Table 7. Slot flow parameters at different depths (H = 1mm, ΔP = 10 pa).

Differential Reynolds Number Gap Depth d (mm) Gap Height h (mm) Air Velocity v (m/s). Pressure (pa) Re 30 10 1 1.351 216.48 50 10 1 0.910 146.01 70 10 1 0.677 108.69

Sustainability 2020, 12, 1708 15 of 20 sizesFigure are 19. mainly Penetration affected rate of by each a gravity particle settlement. size segment The at different larger gap gap depth depths increases (Δ P = 10 the pa, residenceh =1 mm) time of particles in the gap of the envelope, thus increasing the probability of particles contacting the gap wall. 4.3.3. Influence of Pressure Difference between the two Sides of the Gap on the Penetration 4.3.3.Coefficient Influence of Pressure Difference between the two Sides of the Gap on the Penetration Coefficient When the air inlet temperaturetemperature isis 263263 k,k, hh == 1 mm, W = 0.50.5 m, m, d d = 3030 mm, mm, only consider the gap on both sidessides ofof thethe didifferential.fferential. ∆ΔP does not influenceinfluence particleparticle penetrationpenetration rate. At the same time, the variationvariation of of penetration penetration coe coefficientfficient P caused P caused by the by change the change of particle of particle size in diversesize in gapdiverse pressure gap dipressurefference difference (5, 7, 10 pa) (5, was 7, 10 simulated pa) was in simulated this paper. in Inthis∆P paper.= 5 pa, In∆ PΔ=P 7= pa5 pa, cases, ΔP the = 7 velocity pa cases, vector the andvelocity pressure vector vector and pressure of the airflow vector areof the as shownairflow inare Figures as shown 20– in23 Figures respectively., 20–23 respectively., when the pressure when ditheff erencepressure between difference the two between sides ofthe the two gap sides changes, of the the gap change changes, law the of penetration change law rate of haspenetration diverse particlerate has sizesdiverse (Figure particle 24). sizes (Figure 24).

Sustainability 2020, 12, 1708 17 of 21 Sustainability 2020, 12, 1708 17 of 21 Sustainability 2020, 12, 1708 17 of 21 FigureFigure 20.20. Velocity vectorvector ((∆Δ PP == 5 pa).

Figure 21. Pressure vector (Δ P = 5 pa). Figure 21. Pressure vector (Δ P = 5 pa). Figure 21. Pressure vector (∆Δ P = 55 pa). pa).

Figure 22. Velocity vector (Δ P = 7 pa). Figure 22. Velocity vector ((∆Δ P = 7 pa). Figure 22. Velocity vector (Δ P = 7 pa).

Figure 23. Pressure vector (∆ P = 7 pa). Figure 23. Pressure vector (Δ P = 7 pa). Figure 23. Pressure vector (Δ P = 7 pa). Figure 23. Pressure vector (Δ P = 7 pa).

Figure 24. Penetration rate of each particle size segment at different pressure differences (d = 3 cm, h = 1 Figure 24. Penetration rate of each particle size segment at different pressure differences (d = 3 cm, h = 1 Figuremm). 24. Penetration rate of each particle size segment at different pressure differences (d = 3 cm, h = 1 mm). mm). In Figure 24, the difference in pressure between the two sides of the gap has a great impact on In Figure 24, the difference in pressure between the two sides of the gap has a great impact on the penetrationIn Figure 24, rate the differenceof particles, in pressureespecially between those withthe two particle sides sizesof the ofgap less has than a great 0.1 impactμm. The on the penetration rate of particles, especially those with particle sizes of less than 0.1 μm. The thepenetration penetration rate rateP of ofparticles particles, in theespecially range of those 0.25–2.5 with μ mparticle under sizesdifferent of lesspressure than differences0.1 μm. The is penetration rate P of particles in the range of 0.25–2.5 μm under different pressure differences is penetrationclose to 1, which rate Pincreased of particles along in with the rangethe pressu of 0.25–2.5re difference μm under between different the two pressure sides of differences the gap. is close to 1, which increased along with the pressure difference between the two sides of the gap. close to 1, which increased along with the pressure difference between the two sides of the gap. 4.3.4. Influence of Gap Shape on Penetration Coefficient 4.3.4. Influence of Gap Shape on Penetration Coefficient 4.3.4. Influence of Gap Shape on Penetration Coefficient When the air inlet temperature is 263 k, Δ P = 10 pa, h = 1 mm, W = 0.5 m, d = 30 mm, only When the air inlet temperature is 263 k, Δ P = 10 pa, h = 1 mm, W = 0.5 m, d = 30 mm, only consideringWhen the crack air geometryinlet temperature does not is influence 263 k, Δ theP = part 10 iclepa, penetrationh = 1 mm, W rate = 0.5at the m, samed = 30 time. mm, In only this considering crack geometry does not influence the particle penetration rate at the same time. In this consideringpaper, the variation crack geometry of penetration does not coefficient influence Pthe with part particleicle penetration size under rate a atdifferent the same gap time. geometry In this paper, the variation of penetration coefficient P with particle size under a different gap geometry paper, the variation of penetration coefficient P with particle size under a different gap geometry Sustainability 2020, 12, 1708 17 of 21

Figure 21. Pressure vector (Δ P = 5 pa).

Figure 22. Velocity vector (Δ P = 7 pa).

Sustainability 2020, 12, 1708 Figure 23. Pressure vector (Δ P = 7 pa). 16 of 20

Figure 24. Penetration rate of each particle size segment at different pressure differences (d = 3 cm, h = Figure1 mm).24. Penetration rate of each particle size segment at different pressure differences (d = 3 cm, h = 1 mm). In Figure 24, the difference in pressure between the two sides of the gap has a great impact on the penetrationIn Figure rate 24, of the particles, difference especially in pressure those between with particle the two sizes sides of less of the than gap 0.1 hasµm. a Thegreat penetration impact on ratethe Ppenetrationof particles rate in the of rangeparticles, of 0.25–2.5 especiallyµm underthose diwithfferent particle pressure sizes diff erencesof less isthan close 0.1 to μ 1,m. which The increasedpenetration along rate with P of the particles pressure in dithefference range betweenof 0.25–2.5 the μ twom under sides ofdifferent the gap. pressure differences is close to 1, which increased along with the pressure difference between the two sides of the gap. 4.3.4. Influence of Gap Shape on Penetration Coefficient 4.3.4. Influence of Gap Shape on Penetration Coefficient When the air inlet temperature is 263 k, ∆ P = 10 pa, h = 1 mm, W = 0.5 m, d = 30 mm, only consideringWhen the crack air geometryinlet temperature does not is influence 263 k, Δ the P = particle 10 pa, penetrationh = 1 mm, W rate = at0.5 the m, same d = 30 time. mm, In only this paper,considering the variation crack geometry of penetration does not coe influencefficient P thewith part particleicle penetration size under rate a di ffaterent the same gapgeometry time. In this (L, U,paper, square) the wasvariation simulated. of penetration The airflow coefficient parameters P with when particle the airflow size under passes a through different gaps gap of geometry different geometric shapes are shown in Table8. Under the L-shaped and U-shaped seams, the velocity vector and pressure vector of the airflow (Figures 25–30) are present. The law of the penetration rate changes with the different particle size when the gap depth varies (Figure 31). Sustainability 2020, 12, 1708 18 of 21 Table 8. Airflow parameters of different geometries (H = 1 mm, ∆ P = 10 pa). (L, U, square) was simulated. The airflow parameters when the airflow passes through gaps of Aperture Shape Differential Pressure (pa) Gap Height h (mm) Air Velocity v (m/s) Reynolds Number Re different geometric shapes are shown in Table 8. Under the L-shaped and U-shaped seams, the Rectangular 10 1 1.351 216.48 velocityL vector and pressure 10 vector of the airf 1low (Figures 25–30) 1.233 are present. 197.57The law of the penetrationU rate changes with 10 the different partic 1le size when the 1.114 gap depth varies (Figure 178.5 31).

FigureFigure 25. Velocity25. Velocity vector vector of L-shaped of L-shaped gap. gap.

In Figures 26 and 29, although the flow in the L-shaped and U-shaped gaps is laminar flow, turbulence still occurs at the corner. In Figure 31, the larger the n value is, the smaller the particle penetration rate will be, mainly because the airflow disturbance occurs at the gap corner, which increases the probability of collision between particles and the wall surface. The L-shaped and U-shaped gaps have a better blocking effect on larger and smaller particles than the rectangular shape.

Figure 26. Corner velocity vector of L-shaped gap.

Figure 27. Pressure vector of L-shaped gap.

Figure 28. Velocity vector of U-shaped gap. Sustainability 2020, 12, 1708 18 of 21 SustainabilitySustainability 2020 2020, 12, 12, 1708, 1708 1818 of of 21 21 (L, U, square) was simulated. The airflow parameters when the airflow passes through gaps of (L, U, square) was simulated. The airflow parameters when the airflow passes through gaps of different(L, U, square) geometric was shapessimulated. are Theshown airflow in Table parame 8. Underters when the L-shapedthe airflow and pa ssesU-shaped through seams, gaps the of different geometric shapes are shown in Table 8. Under the L-shaped and U-shaped seams, the velocitydifferent vectorgeometric and shapespressure are vector shown of in the Table airf low8. Under (Figures the 25–30)L-shaped are andpresent. U-shaped The lawseams, of thethe velocity vector and pressure vector of the airflow (Figures 25–30) are present. The law of the penetrationvelocity vector rate changesand pressure with thevector different of the partic airflelow size (Figures when the 25–30) gap depthare present. varies (Figure The law 31). of the penetrationpenetration rate rate changes changes with with the the different different partic particlele size size when when the the gap gap depth depth varies varies (Figure (Figure 31). 31).

Sustainability 2020, 12, 1708 Figure 25. Velocity vector of L-shaped gap. 17 of 20 FigureFigure 25. 25. Velocity Velocity vector vector of of L-shaped L-shaped gap. gap.

Figure 26. Corner velocity vector of L-shaped gap. FigureFigureFigure 26. 26. Corner26. Corner Corner velocity velocity velocity vector vector vector of of L-shaped of L-shaped L-shaped gap. gap. gap.

Figure 27. Pressure vector of L-shaped gap. Figure 27. Pressure vector of L-shaped gap. FigureFigure 27. 27. Pressure Pressure vector vector of of L-shaped L-shaped gap. gap.

Sustainability 2020, 12, 1708 FigureFigure 28. 28.Velocity Velocity vector vector of of U-shaped U-shaped gap. gap. 19 of 21 FigureFigure 28. 28. Velocity Velocity vector vector of of U-shaped U-shaped gap. gap.

(a) (b)

FigureFigure 29. 29.Corner Corner velocity velocity vector vector of of U-shaped U-shaped gap. gap. (a )(a Left) Left corner, corner, (b )(b right) right corner. corner.

Figure 30. Pressure vector of U-shaped gap.

Figure 31. The penetration rate of each particle size segment at different geometric shape gaps (d = 3 cm, h = 1 mm).

Table 8. Airflow parameters of different geometries (H = 1 mm, Δ P = 10 pa).

Differential Reynolds Number Aperture Shape Gap Height h (mm) Air Velocity v (m/s). Pressure (pa) Re Rectangular 10 1 1.351 216.48 L 10 1 1.233 197.57 U 10 1 1.114 178.5

In Figures 26 and 29, although the flow in the L-shaped and U-shaped gaps is laminar flow, turbulence still occurs at the corner. In Figure 31, the larger the n value is, the smaller the particle penetration rate will be, mainly because the airflow disturbance occurs at the gap corner, which increases the probability of collision between particles and the wall surface. The L-shaped and U-shaped gaps have a better blocking effect on larger and smaller particles than the rectangular shape.

5. Conclusions Sustainability 2020, 12, 1708 19 of 21 Sustainability 2020, 12, 1708 19 of 21

(a) (b) (a) (b) Sustainability 2020Figure, 12, 1708 29. Corner velocity vector of U-shaped gap. (a) Left corner, (b) right corner. 18 of 20 Figure 29. Corner velocity vector of U-shaped gap. (a) Left corner, (b) right corner.

Figure 30. Pressure vector of U-shaped gap. FigureFigure 30. 30.Pressure Pressure vector vector of of U-shaped U-shaped gap. gap.

Figure 31.31. The penetration rate of each particle size segment at didifferentfferent geometricgeometric shapeshape gaps (d(d= = 3 Figure 31. The penetration rate of each particle size segment at different geometric shape gaps (d = 3 cm,cm, hh= = 11 mm).mm). cm, h = 1 mm). 5. Conclusions Table 8. Airflow parameters of different geometries (H = 1 mm, Δ P = 10 pa). The mass concentrationTable 8. Airflow I/O parameters ratio of indoor of differ andent outdoorgeometries particles (H = 1 mm, and Δ theP = 10 linear pa). regression of Differential Reynolds Number massAperture concentration Shape wereDifferential analyzed. AccordingGap Height to the h (mm) measured Air gap Velocity types ofv (m/s). the building Reynolds envelope, Number a Aperture Shape Pressure (pa) Gap Height h (mm) Air Velocity v (m/s). Re fluent software was usedPressure to simulate (pa) the change of particle penetration coefficient with particleRe size Rectangular 10 1 1.351 216.48 underRectangular different influencing factors;10 the influence law 1 of gap geometry, size, 1.351 and pressure of indoor 216.48 and L 10 1 1.233 197.57 outdoor onL the penetration coe10ffi cient was analyzed. 1 The main conclusions 1.233 are as follows: 197.57 U 10 1 1.114 178.5 (1) WhenU buildings are exposed10 to a high concentration 1 of outdoor 1.114 particles for a long178.5 duration, indoor particles will reach high concentration; by comparing the I/O ratio of measuring points A and B, In Figures 26 and 29, although the flow in the L-shaped and U-shaped gaps is laminar flow, it can beIn observedFigures 26 that and measuring 29, although point the A flow is less in thanthe L-shaped measuring and point U-shaped B; by comparing gaps is laminar the fitting flow, turbulence still occurs at the corner. In Figure 312 , the larger the n value is, the smaller the particle degreeturbulence of points still Aoccurs and B,at wethecan corner. see thatIn Figure the R 31of, pointthe larger B is greaterthe n value than is, that the of smaller point A, the because particle penetration rate will be, mainly because the airflow disturbance occurs at the gap corner, which thepenetration air tightness rate of will building be, mainly envelope because at point the Aairflow is better disturbance than that occurs at point at B, the which gap weakenscorner, which the increases the probability of collision between particles and the wall surface. The L-shaped and correlationincreases degreethe probability of indoor of and collision outdoor between particle concentration.particles and the wall surface. The L-shaped and U-shaped gaps have a better blocking effect on larger and smaller particles than the rectangular U-shaped(2) According gaps have to fluenta better simulation blocking results,effect on the larger penetration and smaller rate particles of particles than in the the rectangular range of shape. 0.25–2.5shape. µm particle size is close to 1, when the gap height h is greater than 0.5 mm. Moreover, when h =1 mm, the penetration rate of particles with particle size ranging from 0.01 to 10 µm exceeded 95%. 5. Conclusions When5. Conclusions h = 0.5 mm, the penetration rate of particles within the range of 0.25–2.5 µm exceeded 90%. When h = 0.1 mm, the penetration rate was the highest when the particle size was around 0.4 µm, and the penetration rate of the particles was about 50%. (3) According to fluent simulation results, the penetration rate of particles at different gap depths within the particle size range of 0.1–1 µm is close to that at different gap depths. When the particle size is less than 0.1µm, the penetration rate decreases with the increase of gap depth d; when the particle size is greater than 2.5 µm, the penetration rate decreases with the increase of gap depth. (4) The fluent simulation result shows that within 0.25–2.5 µm, particles under different pressure differentials within the scope of the penetration rate of P are close to 1; in the gap on both sides of the differential value ∆P, the greater the particle penetration rate, the larger the number n of right-angle number of gaps, and the smaller the penetration rate of particles. The L-shaped and U-shaped gaps have a significantly better barrier effect on larger and smaller particles than the rectangular gap. Sustainability 2020, 12, 1708 19 of 20

Author Contributions: Author Contributions: L.Y. proposed the innovative points and conceives the study. L.Y. and N.K. wrote the paper. W.W., H.G. and J.J. experimented. Y.L. and N.K. revised the paper. All authors have read and agreed to the published version of the manuscript. Funding: The research work is supported by National Key R&D Program of China: 2016YFC0700100 and Key projects of Shenyang Academy of Environmental Sciences: 15-10-154. Acknowledgments: In this section you can acknowledge any support given which is not covered by the author contribution or funding sections. This may include administrative and technical support, or donations in kind (e.g., materials used for experiments). Conﬂicts of Interest: The authors declare no conﬂict of interest

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