Statistical Analysis Approach of Single-sided Ventilation Based on Particle Track Technique Using Large Eddy Simulation

. The main objective of this study is to investigate the airflow characteristics in single-sided ventilation. A CFD method of large eddy simulation (LES) using particle track technique was conducted in this study, and the simulation results are validated by experiment results. The mostly used ventilation efficiency indicators of natural ventilation are Air Flow Rate (AFR) and Purging Flow Rate (PFR). AFR is the volumetric airflow exchange rate through the openings and PFR is the effective airflow rate that removes indoor air pollutants. The ventilation efficiency ( (cid:2) (cid:3) ) of natural ventilation, which is defined as the ratio of PFR and AFR, is not well investigated in previous research, therefore, this study discusses the case of the (cid:2) (cid:3) of single-sided ventilation and tries to explain the distinction between AFR and PFR by statistical analysis approach based on particle movements. Particles are emitted from the opening and the particles’ movements are tracked by tracing their locations at different time steps. The residence time measures the time between the time that particles enter the room and the time that particles leave the room, and indoor travel distance indicates the sum of the displacement when the particle travels in the room. The Probability Density Function (PDF) of the residence time and indoor travel distance is used to depict airflow characteristics of the ventilation path of single-sided ventilation. The analysis method of study might be another useful approach to studying natural ventilation in detail.


Introduction
The properly designed natural ventilation system can efficiently improve indoor air quality, and thermal comfort and save building energy consumption. To evaluate the efficiency of a natural ventilation system, the ventilation rate should be measured on-site or simulated by CFD simulations. There are two usually used ventilation rate indicators: Air Flow Rate (AFR) and Purging Flow Rate. AFR is the volume rate that passes through the opening, which indicates the volume of air exchanged indoors and outdoors in a particular unit of time. PFR measures the volume of indoor contamination that is removed from indoors in a particular unit of time. In the conventional ventilation prediction method: Orifice equation is used to predict the volume flow rate AFR, which, sometimes can not reflect the real ability to remove indoor pollution. However, AFR is difficult to measure in real buildings or wind tunnel tests. The CFD has become a powerful tool to simulate natural ventilation and it makes it possible to compare both AFR and PFR easily. RANS (Reynolds-averaged Navier-Stokes equations) is the mostly used turbulence model in natural ventilation study, but it underestimates the ventilation rate as it neglects the fluctuation components which is of great importance for the turbulence-induced ventilation that dominates the buildings with two openings that have small mean wind pressure coefficient difference. LES * Corresponding author: jiang_zitao@arch.eng.osaka-u.ac.jp (Large Eddy Simulation) is proven to provide better prediction accuracy and transient characteristics in previous research [1]. In addition, the particle track method is a useful method to study the fluctuating airflow characteristics of both mechanical ventilation [2] and natural ventilation [3]. This study aims to present a new perspective to analyse the airflow characteristic of natural ventilation by statistical interpretation of particle track in LES simulations.

Description of experiment
Jiang and Kobayashi reported wind experiment measurements of single-sided and double-sided ventilation in the atmospheric boundary layer wind tunnel at Osaka University [4]. The mean velocity profile and turbulent kinetic energy measured by a constant-temperature hot-wire anemometer with I type probe (0251R-T5, Kanomax) are depicted in Fig 1. The mean velocity profile can be described by a power law: Where Z is the height from the floor. Uz is the mean stream-wise velocity at height of z. UH is the reference wind velocity at the building height H (= 0.1 m), UH= 5.76 m/s. is the power-law coefficient, which is dependent on the roughness of the terrain.
‫ܥ‬ ఓ is a model constant equal to 0.09, L is the turbulent length scale, which is the product of the integral time scale and the mean velocity estimated by Taylor's frozen turbulence hypothesis ‫ܮ‬ = ܶ ௨ ‫ݑ‬ ത, where ܶ ௨ is the integral time scale. The integral time scales (ܶ ௨ ) are a measure of the duration for which the large eddies remain correlated, and it was calculated as Eq.
is the autocorrelation function of streamwise velocity. The autocorrelation function is integrated with respect to time between the limits ߬ = 0 and the first time ܴ ௨௨ (߬) = 0.
The random flow generation technique based on Smirnov's method (spectral synthesizer) [5] was used to generate turbulence inflow for LES simulation.

Computation geometry, domain
Four single-sided ventilation cases were simulated in this study (Fig. 2). The building model size is the same as the building model used in the wind tunnel test. The size of model is ‫)ܮ(1.0‬ × 0.1(ܹ) × ‫)ܪ(1.0‬ ݉ ଷ for 1-1 case and ‫)ܮ(2.0‬ × 0.1(ܹ) × ‫)ܪ(1.0‬ ݉ ଷ for 1-2 case, the size of the opening is 0.015 × 0.015 ݉ ଶ and the distance between the two centres of openings is 0.4 times the wall length. The openings are located either at the windward wall or leeward wall to compare the difference between front single-sided ventilation and back single-sided ventilation. The 1-2BSS case is used as a base case to do grid analysis and validation. The dimensions of the computation domain were chosen based on AIJ guidelines [6], which results in a dimension of ‫)ܮ(7.1‬ × 1.3(ܹ) × ‫)ܪ(6.0‬ ݉ ଷ (Fig. 3). The simulations were performed with the commercial CFD code 2022 R2. The standard ݇ െ ߝ model was used to obtain steady solutions as initial conditions for LES simulation. For LES simulation, a PISO solver was used. Table 1 shows the details of CFD simulation settings. The time step of LES calculation is set to 1 × 10 ିସ s, which ensures the maximum Courant number is smaller than 1. The first 2 s of the LES simulation during when the velocity field transits from steady state to unsteady steady were discarded. The number of time steps used in the main calculation is 1 × 10 ହ , which corresponds to 10 s, i.e. around 35.7 times of flow through time (ܶ = ‫ܮ‬ ܷ ு Τ = ‫,ݏ82.0‬ with ‫ܮ‬ being the streamwise length of the computational domain and ܷ ு being the reference velocity at building height). Fig. 4 shows the average streamwise velocity at the centre of two openings versus sampling time in coarse grid cases. The mean streamwise velocity reaches stability after 6 s (20 T), which indicates the simulation time of LES simulation (35.7 T) is sufficient to obtain statistically steady results.

Grid sensitivity of the base case
Grid sensitivity analysis is conducted based on LES with three different grids of base case (1-2BSS). The coarse, medium and fine grids have 947,758 cells, 1,697,460 cells and 2,529,936 cells respectively. The wall thickness at the opening is divided into 2, 3 and 4 cells and the width of the opening is divided into 5, 10 and 15 cells respectively. Fig. 5 shows the grid analysis results which compare the dimensionless streamwise velocity at three y-direction lines (x=-0.06m, x=0m, x=0.06m) and one x-direction line (y=0.04m). The grid-convergence index (GCI) proposed by Roache [6] is used to quantitively evaluate the error of ܷ ௫ ܷ ு Τ in coarse grid compared to fine grid. GCI is defined as: Where ‫ܨ‬ ௦ is a factor of safety set to 1.25 as to compare three grids, ‫ݎ‬ is the grid refinement ratio (3 for coarse grid and 1.5 for medium grid), p is the formal order of accuracy which is 2 as the second-order discretization schemes used in the simulation. The GCI can estimate the order of convergence and check that the solutions are within the asymptotic range of convergence. The GCI of basic grid results at four lines is shown in Fig. 5. The mean GCI values of four lines are 1.3%, 0.5%, 1.0%, and 1.1% respectively, which show that simulation results are nearly grid independent among three grid systems, therefore, the coarse grid is used in the remainder of the study to reduce the computation cost.

CFD validation
The streamwise velocity around the 1-2BSS building was measured by a Split-fiber film probe (55R56, Dantec Dynamics), which is used to validate the CFD simulation results. Fig. 6 shows a comparison of dimensionless x-velocity components ( ܷ ௫ ܷ ு Τ ) and dimensionless fluctuations of x velocity components ( ‫ݑ‬ ௫ି௦ ܷ ு Τ ) between LES simulation results and experiment results measured by a Split-fiber film probe. The LES simulation results generally agree well with the experiment results despite the velocity fluctuation being underestimated at several points in the LES simulation. .

Ventilation performance evaluation
AFR is defined as the time average of instantaneous volume rates that pass through the openings, which include the transient inverse flow at the opening. ܳ ிோ is calculated by following Equation 7.
‫ݑ‬ ௫, is the velocity components that are perpendicular to the opening, ο‫ܣ‬ is the area of each mesh. A passive gas that has the same property as air is released uniformly from the indoor volume at a rate of M (݇݃/݉ ଷ ) to obtain ܳ ிோ . ܳ ிோ is estimated from the transient indoor volume-averaged concentration C(t) by using the least square method according to Equation 8.
The ventilation rate is normalized by reference velocity at the building height (ܷ ு ) and characteristic opening areas ‫ܣ(‬ = 0.0159݉ ଶ ).
The ventilation efficiency (ߝ ௩ ) is defined as the ratio of ܳ ிோ and ܳ ிோ as Equation 11 [7]. It indicates the percentage of airflow rate that contributes to the removal of indoor contaminants. Table.
3 compares dimensionless ventilation rates and ventilation efficiency between four cases. The building aspect ratio of 1:2 has a higher ventilation rate than that of 1:1, and FSS cases have higher ventilation rates than BSS cases, which shows the same trend with the wind tunnel test.

Particle setting
Massless particles are emitted from five points of one of the openings in each case. Fig. 7 shows the emission points in 1-1FSS and 1-1BSS. A total of 100,000 particles are released during the first 2 s at an interval of 0.0001s. The release period was determined by the time characteristic of velocity fluctuation at the opening centre (around 0.33s), therefore it should be long enough to reflect the statistical characteristic of the airflow. The particles were tracked every 0.001s during the whole calculation time (10s) to reduce the computation resources.

Fig. 7. Particle emission example of 1BSS cases
The trajectory information of each particle can be extracted from the locations of all particles at each time step. Fig. 8 shows the particle distributions at t=0.5s of the 1-1BSS case.   Fig. 8. Particle distribution at t=0.5s of 1-1BSS Fig. 9. Particle (centre of opening) trajectory example Fig. 9 shows the example of the trajectory of particles emitted at the centre of the opening at t=0/0.0001/0.0002s in 1-1 FSS and 1-1 BSS respectively. The trajectory varies even if the emission time difference is merely 0.0001s. To analyse the particle track results, the probabilistic view is an important tool to interpret complicated trajectory information. Fig. 10 shows the vertical airflow characteristic difference between 1-1FSS and 1-1BSS by LES transient velocity contour and typical particle track trajectory example. It can be seen that the inflow of FSS tends to flow downward while the inflow of BSS tends to flow upward, which is a consequence of the front and back vortex generated next to the openings. Fig. 11 is the mean velocity vector around a sealed building without openings and the vortex can be identified. The inflow direction characteristic can also be observed in Fig. 12, which shows the probability distribution of the velocity angle at the centre of the opening. The highest probability concentrates around -90° (z-downward direction) in FSS and +90 (z+ upward direction) in BSS.   13 shows two types of particle movement patterns at the horizontal plane which indicate the indoor airflow pattern. Type 1 is the particle mainly recirculated within half of the room and leaves the room through the same opening as it entered. Type 2 is the particle that travels through the indoor space and leaves the room through the opposite opening. The percentage of particles that enter or leave each opening is summarized in Table 4. The high percentage of Type 1 shows that the recirculating flow is dominating in single-sided ventilation. The building aspect ratio of 1:2 has a higher recirculate flow percentage than 1:1 which results from the larger opening distance.  Fig. 13. Percentage of two types of movements The fluctuating pressure difference between indoors and outdoors drives the air to move in and out through the openings. Fig. 14 shows the instantaneous inflow ܳ ிோ Ԣ and outflow ܳ ிோ Ԣ at the same opening of 1-1BSS. The overlapping area indicates inflow and outflow happen at the same opening, which is the eddy penetration phenomenon. Fig. 15 is the snapshot of the velocity vector at one opening of 1-1BSS, and the vortex at the opening can also be observed. The eddy happens at the transition between inflow and outflow. The eddy generated at the opening helps to bring the fresh air to mix the indoor pollution and brings the mixed air out of the room.    Fig. 16 shows the example of three types of particles of the 1-1BSS case. The return probability ‫ݎ(‬ ) is defined as the number of particles that return to the room i times versus the total number of particles that enter the room. ‫ݎ‬ means the particle only enters once, ‫ݎ‬ means particle enters the room twice and so on. Table. 5 shows the return probability of each case. The spatial vortex and temporal velocity fluctuations around the opening make the particles recirculate around and sometimes return to the room after once leaving. Indoor residence time (߬ ) and the indoor travel distance (l) of each particle is calculated. Indoor travel distance is the sum of displacements of each particle between time steps Dimensionless indoor travel distance (݈ ᇱ ) is indoor travel distance(l) normalized by building height (H). Fig. 17 shows the example of dimensionless travel distance probability density of 1-1BSS case. There is three peak probability which corresponds to particle trajectory A, B and C. Peak A is mainly the short circuit particles that enter the room and then immediately leave the room. Peak B has a ݈ ᇱ of 2.78, which is 2.78 times the height of the building, the particle flows to the deepest part of the room and leaves the room with the outflow of air. Peak C has ݈ ᇱ of 5.2993, and the particle is recirculated before leaving the room. D is an example of particles that have a long trajectory which is recirculated for a long period. Fig. 17. Example of peak probability particle trajectory  . 18 compares the Indoor residence time and dimensionless indoor travel distance of each case. The high peak of brief residence time and short dimensionless travel distance can be observed in all cases, which are regarded to be a characteristic of singlesided ventilation. Compared to dimensionless travel distance, the peak of residence is less obvious, and probability is somewhat more uniform.

Conclusion
In this study, LES simulations using the particle track method were performed to study the airflow characteristic of single-sided ventilation. It is proved that FSS has a better ventilation performance than BSS. The inflow air direction is downward in FSS and upward in BSS due to the influence of the vortex windward and leeward of the building. The opening velocity and particle movement statistics show that pulsation and mixing theory both play a role in single-sided ventilation. The probabilistic view of particle track movement provides a new perspective to interpret and study airflow in natural ventilation.