Experimental measurements and large eddy simulation of particle deposition distribution around a multi-slot diffuser

Building and Environment 150 (2019) 156–163

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Experimental measurements and large eddy simulation of particle deposition distribution around a multi-slot diffuser

T

Yue Pana, Chao-Hsin Linb, Daniel Weic, Chun Chena,d,∗ a

Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T, 999077, Hong Kong, China Environmental Control Systems, Boeing Commercial Airplanes, Everett, WA, 98203, USA c Boeing Research & Technology, Beijing, 100027, China d Shenzhen Research Institute, The Chinese University of Hong Kong, Shenzhen, 518057, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Indoor environment Computational fluid dynamics (CFD) Aerosol Lagrangian tracking Aircraft cabin environment Indoor particle

Enhanced soiling around multi-slot air diffusers due to particle deposition is frequently observed in commercial airplanes. The dirty black soiling is very unsightly and influences the passengers’ perception of cabin air quality. This study conducted experimental measurements and large eddy simulations with Lagrangian tracking for the distribution of particle deposition around a multi-slot diffuser. This investigation first used a relatively simple case of indoor particle deposition to compare the LES-Lagrangian model with the RANS-Lagrangian model with near-wall turbulence kinetic energy correction. The comparison shows that the LES-Lagrangian model was more robust than the RANS-Lagrangian model in predicting particle deposition indoors. The superior LES-Lagrangian model was then applied in predicting the particle deposition distribution around a multi-slot diffuser. This investigation also conducted detailed measurements of the distribution of particle deposition around the multislot diffuser in a laboratory chamber using a wiping method on a resolution of 3 × 20 mm2. The measurement accuracy of the wiping method was within 20%. The particle deposition distribution predicted by the LESLagrangian model was compared with the experimental data to validate the model. The results indicated that the LES-Lagrangian model correctly predicted the order of magnitude of the particle deposition velocity distribution around the multi-slot diffuser with an average relative error of 63.2%.

1. Introduction Exposure to indoor particles from infiltration [1–6] and indoor sources [7–11] is strongly associated with adverse health effects [12–14]. Particle deposition is an important indoor transport process that has mixed effects on our daily lives [15]. On one hand, particle deposition decreases the number of suspended airborne particles indoors [16]. Consequently, indoor exposure and the associated health risks are reduced [17]. On the other hand, particle deposition may cause damage to and discoloration of indoor surfaces [18]. A widely observed phenomenon is the enhanced soiling of indoor surfaces caused by particle deposition [19,20]. This soiling is very unsightly and reduces our quality of life. It is worthwhile to investigate the mechanisms of enhanced particle deposition in order to improve the design of indoor environment and prevent the soiling problem. Enhanced soiling is often seen at the corners of walls/ceiling, on the walls/ceiling above a heater or lamp, and on the wall/ceiling around an air diffuser. Salthammer et al. [19] and Fittschen et al. [20] suggested

∗

that the concentration of semi-volatile organic compounds was a determinant of enhanced soiling. Timmer and Zeller [21] conducted numerical simulations to estimate the amount of particle deposition around a ceiling induction outlet. The local airflow characteristics were identified as the decisive factor. Chen and colleagues [22,23] experimentally and numerically studied particle deposition on the wall above a heater. The amount of particle deposition was found to be positively correlated with a large temperature differential. As a result of inappropriate design, enhanced soiling around air diffusers is also often seen in building environments. The source of the deposition has been found to be indoor suspended particles [24,25]. These studies have provided great insight into the problem of enhanced soiling in indoor environments. Multi-slot diffusers, which are widely used in aircraft cabins [26–28], are at high risk of enhanced soiling if the design is inappropriate. As a matter of fact, enhanced soiling around multi-slot diffusers due to particle deposition is frequently observed in commercial airplanes. The dirty black soiling is very unsightly and influences

Corresponding author. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N.T, 999077, Hong Kong, China. E-mail address: [email protected] (C. Chen).

https://doi.org/10.1016/j.buildenv.2019.01.011 Received 22 November 2018; Received in revised form 7 January 2019; Accepted 8 January 2019 Available online 09 January 2019 0360-1323/ © 2019 Elsevier Ltd. All rights reserved.

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Fig. 1. Schematic of the mechanisms of near-wall particle deposition around a multi-slot diffuser.

computational cell, and G(x, x') is a localized function for the filtering, which is defined as:

passengers’ perception of cabin air quality. Chen et al. [29] used a Reynolds-averaged Navier-Stokes (RANS) eddy-viscosity model with Lagrangian tracking to calculate the particle deposition around a multislot diffuser. Cao et al. [30] further applied the model to estimate particle deposition around the cabin air supply nozzles in commercial airplanes. In general, as illustrated in Fig. 1, at the locations near the slot dividers (shown in red), strong turbulent diffusion toward the wall creates a high possibility of particle deposition. However, at the slot openings (shown in blue), the particles are blown away by the strong jets before they have a chance to deposit on the wall. Although several studies have focused on particle deposition around multi-slot diffusers, both the experimental and numerical studies are far from complete. First, the eddy-viscosity model used in the previous studies [29,30] assumed the turbulence to be isotropic around multislot diffusers. In order to correct the prediction of the fluctuating velocity in the wall-normal direction in the near-wall cells, damping functions were used to modify the near-wall turbulence kinetic energy. However, the accuracy may have been significantly influenced by the dimensionless wall distance, y+. Therefore, to increase the robustness of the simulations, it is worthwhile to utilize non-isotropic turbulence models, such as large eddy simulation (LES), to calculate the particle deposition around multi-slot diffusers. Second, although numerous studies have collected experimental data on particle deposition velocities [e.g. Refs. [31–39]], very little, if any, measured data on detailed particle deposition distribution is available in the literature. As there are specific patterns to the enhanced soiling around a multi-slot diffuser due to particle deposition, detailed experimental data on particle deposition distribution is essential for both quantification and model validation. Therefore, this study aimed to conduct experimental measurements and large eddy simulations with Lagrangian tracking for the distribution of particle deposition around a multi-slot diffuser. This investigation first compared LES and the RANS eddy-viscosity model with modified near-wall turbulence kinetic energy to confirm the superiority of the LES-Lagrangian model. This study then conducted detailed measurements of the distribution of particle deposition around a multislot diffuser in a laboratory chamber. Finally, this investigation used the LES-Lagrangian model to calculate the distribution in the experimental case and compared the results with the experimental data for model validation.

1

G (x , x ′) =

x ′otherwise

(2)

where Vcell (m ) is the volume of the computational cell. Note that G(x, x') is a positive value only when x’ is within the computational cell. Flow eddies larger than the computational cell length scale are regarded as “large eddies”, and those smaller than the length scale are regarded as “small eddies”. After filtering, the mass continuity and momentum governing equations are:

∂u¯ i =0 ∂x i

(3)

1 ∂ 1 ∂p¯ 1 ∂τij ∂u¯ i ∂ (u¯ i u¯ j ) = (σi j ) − − + ρ ∂x j ρ ∂x i ρ ∂x j ∂t ∂x j

(4)

where ui and uj (m/s) are the components of the fluid velocity in the xi and xj (m) directions, respectively, t (s) is the time, ρ (kg/m3) is the air density, p (Pa) is the air pressure, σij (kg/s2m) is the stress tensor due to molecular viscosity, and τij (kg/s2m) is the subgrid-scale Reynolds stress. The bars in Eqs. (3) and (4) represent the filtering of the grid. The subgrid-scale Reynolds stress in Eq. (4) is defined as

τij = ρ (ui uj − u¯ i u¯ j )

(5)

which is unknown and must be modeled. This investigation used the Smagorinsky subgrid-scale model [40] to determine the subgrid-scale Reynolds stress. The model assumes that the stress is proportional to the strain rate of the tensor:

τij = −2υSGS S¯ij

(6)

where the strain rate of the tensor is:

∂u¯ j ⎞ 1 ∂u¯ S¯ij = ⎛⎜ i + ⎟ ∂x i ⎠ 2 ⎝ ∂x j

(7)

and υSGS is the subgrid-scale eddy viscosity, which is defined as:

υSGS = (CSGS Δ)2 (2S¯ij S¯ij )1/2

(8)

where CSGS is the Smagorinsky constant. Note that LES is transient in nature. For particle dispersion and deposition, this study utilized the Lagrangian method, which has been widely used [e.g. Refs. [41–43]] in the past, to calculate the trajectory of each particle on the basis of Newton's law:

2.1. LES-Lagrangian model LES directly solves the filtered Navier-Stokes equations for largescale eddies, while modeling small-scale eddies. The governing equations for LES are obtained by filtering the Navier-Stokes equations. The filtering process effectively excludes small eddies whose scales are smaller than the grid spacing. A filtered variable, ϕ, is defined as:

∫D G (x, x′) ϕ (x ) dx′

x′ ∈ D

3

2. Numerical models

ϕ¯ (x ) =

⎧ Vcell ⎨0 ⎩

→ g (ρp − ρ) → u −→ up ) + = FD (→ +F ρp dt

d→ up

(9)

→ where → u (m/s) is the air velocity, g up (m/s) is the particle velocity, → → (m/s2) is the gravitational acceleration, ρp is the particle density, and F u −→ up) , was cal(m/s2) is the Brownian motion. The drag force, FD (→ culated by:

(1)

where x represents the coordinates, D is the fluid domain in a 157

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FD (→ u −→ up ) =

18μ → → ( u − up ) ρp dp2 Cc

viscosity models assume the turbulence to be isotropic, the fluctuating velocity in the wall-normal direction in the turbulent boundary layer tends to be over-predicted. Therefore, the turbulence kinetic energy in the near-wall cells must be modified. The damping function proposed by Chen et al. [29] was applied in this study:

(10)

where μ is the air viscosity, dp is the particle diameter, and Cc is the Cunningham correction to Stokes' drag law:

Cc = 1 +

dp ⎞ ⎞ λ ⎛ ⎛ ⎜2.514 + 0.8 exp − 0.55 ⎟ dp ⎝ λ ⎠⎠ ⎝ ⎜

2

⎟

(11)

knear _ wall

where λ is the mean free path of air molecules. Note that, at each time step, the air velocity for the particle trajectory calculation is the transient air velocity calculated by LES at that time step. This transient air velocity includes both the time-averaged and fluctuating velocity. Therefore, the turbulence dispersion is naturally considered in the drag force. With the trajectory information for each tracked particle, this study further calculated the local particle deposition velocity for each computing mesh on a surface by Ref. [29]:

vd, i =

Nd, i /(Ai ⋅t ) N¯ / V

(14) ∗

where u is the friction velocity. Modifying the turbulence kinetic energy in the near-wall cells tends to improve the accuracy of the predicted fluctuating velocity in the wall-normal direction. The local particle deposition velocities were calculated using Eq. (12). The RANSLagrangian calculations were conducted using the CFD code ANSYS Fluent 16.0 [44], and user-defined functions were implemented in the program to realize the near-wall turbulence kinetic energy corrections. The assumptions about particle resuspension and smooth surfaces were the same as those for the LES-Lagrangian model.

(12)

where the subscript i represents the ID of a computing cell on a surface, Nd,i is the number of particles depositing onto this cell within the time period t, the variable Ai is the area of the cell, N¯ is the average number of particles in the calculation domain within the time period t, and V is the volume of the calculation domain. The airflow distribution, particle dispersion and deposition were calculated using the computational fluid dynamics (CFD) code ANSYS Fluent 16.0 [44] with several user-defined functions. First, to reduce the computing cost, a RANS model was used to calculate the airflow field as the initial field for the LES calculations. LES was then used to calculate the airflow for a room time constant of 0.5 as recommended by Chen et al. [45] to achieve steady-state conditions. Next, a certain number of particles were released uniformly in the calculation domain. The LES model with Lagrangian tracking was then used to calculate the transient airflow and the particle trajectories simultaneously. At the end of each time step, the local particle deposition velocities were calculated by means of the user-defined functions. For the LES implemented in ANSYS Fluent, the wall boundary conditions have been implemented using a law-of-the-wall approach [44]. However, as LES directly resolves the boundary layer, it is necessary to use a very fine near-wall mesh spacing in order to obtain best results [44]. As recommended in ANSYS Fluent User's Guide, the dimensionless wall distance, y+, should be set at approximately 1 for LES [44]. This study neglected the influence of particle resuspension, as the disturbances in the studied cases were minimal. Therefore, when a particle approached a surface, the trajectory calculation of the particle was terminated as long as it came into contact with the surface. In addition, this investigation assumed the surfaces to be smooth.

3. Model validation and evaluation Theoretically, the LES-Lagrangian model tends to be superior to the RANS-Lagrangian model in predicting particle deposition from the perspective of accuracy and robustness. However, this hypothesis has not been well validated. Before applying the models to multi-slot diffusers, this section first discusses a relatively simple case of particle deposition in a ventilated chamber from the literature [47] that was used in the present study to validate and evaluate the LES-Lagrangian model. The predicted particle deposition rates from the LES-Lagrangian model were compared with the experimental data and the results from the RANS-Lagrangian model in order to examine the accuracy and robustness of the model. Such a simple case can avoid the influence of the complex factors such as irregular geometries, which is beneficial for the model comparison. 3.1. Case setup Bouilly et al. [47] measured the deposition rates for particles with diameters ranging from 0.3 to 15 μm in a ventilated chamber with dimensions of 2.5 × 2.5 × 2.5 m3 under isothermal conditions. As shown in Fig. 2, the supply air inlet was located in the side wall near the floor, and the exhaust was installed in the opposing wall near the ceiling. The sizes of the inlet and exhaust were both 0.07 × 0.07 m2. The measured supply air velocity was 0.44 m/s. The air change rate in the room was 0.5 ACH. A grid-independence test was conducted to ensure that the grid was sufficiently fine to capture the turbulence in the chamber. Both structured and unstructured meshes were tested for both models. Tetrahedral grids were used to generate the unstructured meshes, while

2.2. RANS-Lagrangian model For the sake of comparison, this investigation also used the RANS eddy-viscosity model with Lagrangian tracking (denoted as the RANSLagrangian model) to calculate the particle deposition indoors. The RANS eddy-viscosity model used in this study was the shear stress transport (SST) k-ω model [46] as recommended by Chen et al. [29]. First, the steady-state airflow field was obtained by the SST k-ω model. The Lagrangian model was then used to calculate the particle dispersion and deposition. Since both large and small eddies are modeled in RANS models, the turbulence dispersion of the particles also needs to be modeled. This study used the discrete random walk (DRW) model to consider the turbulence dispersion:

u′i = ζi 2k /3

2

⎧ 3 [u∗ (0.008y+ )] y+ ≤ 2.5 ⎪2 = 3 [u∗ (0.0000029y+3 − 0.000616y+2 + 0.0412y+ − 0.042)2]2 ⎨2 ⎪ 2.5 < y+ ≤ 80 ⎩

(13) Fig. 2. Configuration of the case by Bouilly et al. [39] used for model validation and evaluation.

where u'i is the turbulent fluctuating air velocity, ζi is a standard normal random number, and k is the turbulence kinetic energy. Since the eddy158

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Table 1 Grid numbers and average y+ values for the LES-Lagrangian and RANSLagrangian models with both structured and unstructured meshes. Model

Mesh type

Grid number

Average y+ value

LES-Lagrangian RANS-Lagrangian

Structured Structured Structured Structured Unstructured Unstructured Unstructured Unstructured

1.1 million 3.0 million 0.15 million 0.019 million 1.8 million 6.0 million 0.29 million 0.056 million

1.0 0.5 3.5 8.5 1.0 0.1 1.5 7.0

LES-Lagrangian RANS-Lagrangian

hexahedral grids were used to generate the structured meshes. The growth ratio of the grids from the walls was set at 1.2. Table 1 lists the final grid resolutions and y+ values for the LES-Lagrangian and RANSLagrangian models with both structured and unstructured meshes. Note that the average y+ for LES was set at around 1 as required in Ref. [44]. For the RANS model, the average y+ was set at various values because, theoretically, any y+ within 80 should provide reasonable results according to Eq. (14). Before the particle calculations were conducted, the turbulence kinetic energy in the near-wall cells was modified using Eq. (14) in the RANS-Lagrangian model. For both models, 0.125 million particles with a certain diameter were evenly released into the chamber. The particle trajectories and deposition were calculated with the use of Lagrangian tracking. The calculations were repeated for a total of eight particle sizes ranging from 0.1 to 10 μm.

Fig. 4. Comparison of the particle deposition rates predicted by the LESLagrangian model, RANS-Lagrangian model with different y+ values, and measured data [47] for unstructured meshes.

completely dependent on the existence of the corresponding measured data. Thus, in general, the LES-Lagrangian model was found to be more robust than the RANS-Lagrangian model. Next, Fig. 4 compares the particle deposition rates predicted by the LES-Lagrangian and RANS-Lagrangian models with unstructured meshes, and the data measured by Bouilly et al. [47]. As in the cases with structured meshes, the LES-Lagrangian model predicted the particle deposition rates reasonably well in comparison with the experimental data. In addition, the RANS-Lagrangian model with unstructured meshes was sensitive to the y+ value. Note that the suitable y+ values for the RANS-Lagrangian model with structured and unstructured meshes were 3.5 and 1.5, respectively. Thus, the mesh type affects the suitable y+ for the RANS-Lagrangian model. In contrast, the accuracy of the LES-Lagrangian model was insensitive to mesh type. These results further demonstrate that the LES-Lagrangian model was more robust than the RANS-Lagrangian model. This study used a cluster with 64 cores to calculate the above cases. For the structured meshes, the LES-Lagrangian model took 3.7 h to complete the calculation, while the RANS-Lagrangian took 0.8 h. For the unstructured meshes, the computing time for the LES-Lagrangian model was 5.4 h, while that for the RANS-Lagrangian model was 1.3 h. Therefore, the RANS-Lagrangian model was 3.2–3.6 times faster than the LES-Lagrangian model. However, considering the robustness, the LES-Lagrangian model is still preferable to the RANS-Lagrangian model in predicting particle deposition indoors. Based on this conclusion, this study will directly apply the LES-Lagrangian model to calculate particle deposition around a multi-slot diffuser in the following section.

3.2. Validation and evaluation Fig. 3 compares the particle deposition rates predicted by the LESLagrangian and RANS-Lagrangian models with structured meshes, and the measured data from Bouilly et al. [47]. The LES-Lagrangian model correctly predicted the particle deposition rates as compared with the experimental data. The particle deposition rates remained relatively unchanged as the particles diameter increased from 0.3 to 1 μm. However, as the particle size increased from 1 to 15 μm, the deposition rates increased. For the RANS-Lagrangian model with a y+ of 3.5, the prediction agreed well with the experimental data, but when the y + values were 0.5 and 8.5, respectively, the predicted particle deposition rates deviated significantly from the experimental data. Note that, theoretically, the modified near-wall turbulence kinetic energy determined by Eq. (14) should apply to y+ values up to 80. However, the comparison in Fig. 3 challenges this hypothesis. Namely, the RANSLagrangian model can be used to make predictions only when a suitable y+ has been identified. Furthermore, the accuracy of this approach is

4. Particle deposition distribution around a multi-slot diffuser As discussed in the Introduction, there is a lack of quantitative experimental data on particle deposition distribution in indoor environments. Therefore, as described in the present section, we conducted experimental measurements of particle deposition distribution around a multi-slot diffuser in a chamber. The case was then calculated using the LES-Lagrangian model, since it was found to be more robust than the RANS-Lagrangian model from the previous section. Next, the predicted results were compared with the experimental data to validate the capability of the LES-Lagrangian model in predicting particle deposition distribution around a multi-slot diffuser. 4.1. Experimental setup Fig. 3. Comparison of the particle deposition rates predicted by the LESLagrangian model, RANS-Lagrangian model with different y+ values, and measured data [47] for structured meshes.

This study constructed a chamber with dimensions of 1, 0.5, and 1.4 m in length, width, and height, respectively, as depicted in Fig. 5(a). 159

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ventilation system was operated for half an hour to achieve a stable air distribution. The particles were then continuously released into the cabin from the center point with the use of a dust generator (RBG1000, PALAS Inc, Germany) for 4 h. The PM2.5 concentration in the chamber was measured every second with the particle monitor (DustTrak II 8532) during the experiments. The time-average PM2.5 concentration in the 4-h experiment was 2.52 mg/m3. Both qualitative and quantitative experiments were conducted for the particle deposition distribution around the multi-slot diffuser. In the qualitative experiments, photographs were taken to observe the distribution of particle deposition on the target surface of the diffuser. For visualization of the deposited particles, this study covered the target surface with black paper, as shown in Fig. 6(b), to better reflect the deposited particles which were relatively light in color. In the quantitative experiments, a wiping method proposed by Ref. [48] was used to measure the mass distribution of the deposited particles on the target surface of the multi-slot diffuser. The wiping method made use of Scotch Double Sided 665 tape, which has excellent dustcollection efficiency and low hygroscopic properties. Pieces of the tape were covered with sampling sheets and pressed against the target surface with suitable force. The pieces of tapes were weighed before and after sampling so that the weight of the particles could be determined. A high-precision balance (CPA225D, Sartorious Lab Instruments GmbH &Co.KG 37070, Goettingen, Germany) with an accuracy of 0.01 mg was used to measure the weights of the wiped deposited particles. The target surface shown in Fig. 6(a) was divided into 119 sub-areas, each with dimensions of 3 × 20 mm2. The particle deposition velocity for each sub-area was calculated by:

Fig. 5. (a) Schematic of the chamber for measuring the particle deposition distribution, and photographic images of (b) the multi-slot diffuser and (c) the diffuser outlet.

A multi-slot diffuser for aircraft cabins was fabricated using a 3D printer (Stratasys Fortus 360mc) as shown in Fig. 5(b). The length and width of the diffuser outlet were 356.9 and 29.1 mm, respectively. There were 100 slot openings in the diffuser, as shown in Fig. 5(c). The interval between slots was 5.7 mm, and the width of each slot divider was 1.4 mm. The multi-slot diffuser was installed at ceiling level next to the right-hand wall. The exhaust was located in the left-hand wall at floor level. A variable-speed fan was installed in a soft duct to supply air to the multi-slot diffuser. The supply airflow rate was set as 0.0087 m3/s, and the corresponding air exchange rate was 50.5 ACH. No heat sources were present in the chamber, and the experimental setup was controlled at a constant temperature of 24 °C. The distribution of supply air velocity from the multi-slot diffuser was measured with the use of a traversing mechanism. The automated system, consisting of a step motor, a controller, and a hot-sphere anemometer, achieved precise positioning at a resolution of 2 mm. Fig. 6(a) shows the virtual area of the supply air velocity measurements, which was located 1 cm below the diffuser outlet to avoid the influence of the anemometer on the supply air. There were six measurement lines, as shown in the figure, and each line consisted of 170 measurement points. The horizontal measurement interval was 2 mm, and the longitudinal interval was 5 mm. The total number of measurement points was 1020, which was sufficient for obtaining the detailed supply air velocity distribution at the diffuser outlet. The controller was set to move the anemometer automatically to measure the air velocities at the specified points. The supply air velocity distribution was measured three times to ensure the repeatability of the experiments. Arizona test dust was used as the particle source in the experiments. According to the specifications of the test dust, the mass fraction of particles with diameter less than 2.5 μm was 98%. Therefore, it can be well regarded as PM2.5 (particulate matter with aerodynamic diameter less than 2.5 μm). The representative size for the dust was 1 μm, and the size distribution was known. Before the start of each experiment, the

vd,exp, i =

mexp, i ∗ Cin,exp texp

(15)

where mexp,i is the measured weight of the particles deposited onto the sub-area, Cin,exp is the measured particle concentration in the chamber, and t∗exp is the period of system operation. 4.2. Verification of the wiping method To verify the feasibility of the wiping method, the study conducted a series of preliminary measurements of particle deposition onto small surfaces. First, a certain amount of Arizona dust was measured with the high-precision balance to obtain the benchmark particle weight. The dust was then loaded onto a small surface with an area of 3 × 10 mm2. The weight of the deposited particles was measured using the wiping method and compared with the benchmark, as shown in Fig. 7(a). This test was repeated 18 times with different benchmark particle weights. The relative errors were within 20% for most of the tests. Next, this study evaluated whether the accuracy of the measurements would be affected if there were adjacent areas to be measured. A surface consisting of five sub-sections, each with an area of 3 × 10 mm2, was used for the tests. The dust was loaded onto each sub-section individually, and the benchmark particle weights were obtained in advance. The weights of the deposited particles on each sub-section were then measured using the wiping method and compared with the benchmark, as shown in Fig. 7(b). The results show that the relative errors in most cases were within 20%, which was comparable to most of the indoor

Fig. 6. Schematics of (a) the virtual area and (b) the measurement area of particle deposition distribution. 160

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Fig. 7. Comparison of the measured particle deposition using the wiping method with the benchmark data: (a) a single area and (b) multiple areas.

particle deposition measurements in previous studies (e.g. Ref. [47]). Therefore, the wiping method was also effective when there were adjacent areas that needed to be measured. These preliminary measurements demonstrated the accuracy of the wiping method, and it was subsequently used in measuring the distribution of particle deposition around the multi-slot diffuser installed in the chamber.

4.3. Comparison between simulation and experiment This study used the LES-Lagrangian model to calculate the distribution of particle deposition velocity around the multi-slot diffuser. First, a grid-independence test was conducted to determine the suitable grid resolution. The final grid number of the unstructured mesh was 6.1 million with an average y+ of 1. This study then used the RANS model to calculate the airflow field as the initial field. Next, LES was used to calculate the transient airflow for 140 s of flow time to achieve steadystate conditions [45]. A total of 6.4 million particles with a certain diameter were evenly released in the chamber; this quantity was sufficient to obtain particle-number-independent results [49]. The transient airflow and particle trajectories were calculated using LES with Lagrangian tracking, and the local particle deposition velocity distribution was calculated by Eq. (12). The particle calculations were repeated for six particle sizes ranging from 0.8 to 2.5 μm. The local particle deposition velocity for PM2.5 was then calculated as a weighted average according to the size distribution of the Arizona dust. Fig. 8 compares the supply air velocity contour in the virtual measuring area obtained from the experiment and numerical simulation. The measured supply air velocity distribution contained 1020 data points of measured velocity. The predicted velocity distribution from LES was obtained by averaging the time-resolved velocities for one room time constant under steady-state conditions. In general, the supply air velocity distribution predicted by LES reasonably matched

Fig. 9. Qualitative comparison of the particle deposition distribution: (a) a photographic image from the experiment and (b) the prediction by the LESLagrangian model.

the experimental data. Quantitatively, the average relative error of the predicted air velocity for the 1020 points was 19.4%, and the standard deviation of the relative errors was 14.7%. Fig. 9 compares a photographic image of the particle deposition pattern obtained from the experiments and the particle deposition distribution predicted by the LES-Lagrangian model. Both the experiment and simulation showed that heavy particle deposition occurred in the areas under the slot dividers, while very little particle deposition was found in the areas under the openings. Thus, the LES-Lagrangian model correctly predicted the qualitative distribution of particle deposition around the multi-slot diffuser. Next, Fig. 10 compares the particle deposition distribution predicted by the LES-Lagrangian model and the data measured with the wiping method. There were a total of 119 measurement areas, each with a size of 3 × 20 mm2 and corresponding to a slot opening or a slot divider of the diffuser. For each area, the weight of the deposited particles was measured. The particle deposition velocity was then calculated using Eq. (15). To our best knowledge, this work is the first to measure the particle deposition velocity distribution indoors with such a small resolution. For the simulation, the average particle deposition velocity for each measurement area was calculated in order to compare them with the measured data. The comparison shows that the LES-Lagrangian model predicted the particle deposition velocity pattern reasonably well in comparison with the experimental data. Note that the multi-slot diffuser was 3D printed according to the high-resolution geometry model of a real diffuser used in a commercial airplane. There was a baffle with many holes installed in the diffuser plenum in order to enhance the uniformity of the supply air. However, the holes in the diffuser plenum and slots at the outlet of the diffuser did not exactly correspond to each other. Therefore, the structure of the multi-slot diffuser was not strictly symmetric. Consequently, both the experiment

Fig. 8. Comparison of the supply air velocity distribution contour: (a) the measured data from the experiment and (b) the prediction by LES. 161

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deposition. Third, if the problems with the existing multi-slot diffusers cannot be remedied, reducing the indoor particle concentrations is an effective means of reducing the total number of deposited particles [25]. Indoor filtration using either traditional HVAC filters [60,61] or novel nanofiber filters [62–66] can effectively reduce the total particle deposition, but the corresponding energy consumption should be taken into account when such an intervention is used. 6. Conclusions This study conducted experimental measurements and large eddy simulations with Lagrangian tracking for the distribution of particle deposition around a multi-slot diffuser. The investigation first compared the LES-Lagrangian and RANS-Lagrangian models to confirm the superiority of the LES-Lagrangian model. This investigation then conducted detailed measurements of the distribution of particle deposition around a multi-slot diffuser in a laboratory chamber. The particle deposition distribution predicted by the LES-Lagrangian model was compared with the experimental data to validate the model. Within the scope of this research, the following conclusions can be drawn:

Fig. 10. Qualitative comparison of the particle deposition distribution: (a) the measured data from the experiment and (b) the prediction by the LESLagrangian model.

and simulation showed dissymmetric particle deposition patterns. Quantitatively, the average relative error of the particle deposition velocity for the 119 samples was 63.2%, and the standard deviation of the relative errors was 27.8%. In general, the order of magnitude of the particle deposition velocity was predicted correctly. However, more efforts are needed in the future to further increase the accuracy through the development of novel high-accuracy measurement techniques and further improvement of near-slot airflow and turbulence modelling.

(1) The LES-Lagrangian model was more robust than the RANSLagrangian model in predicting particle deposition indoors. (2) The wiping method can be used to measure the detailed distribution of particle deposition velocity around the multi-slot diffuser. (3) The LES-Lagrangian model can predict the particle deposition velocity distribution around the multi-slot diffuser reasonably well. Acknowledgement

5. Discussion This work was partially supported by the National Natural Science Foundation of China (Grant No. 51708474).

There are several limitations of this study. First, although the LESLagrangian model was more robust than the RANS-Lagrangian model, the former model required more computing resources because the grid number with y+ of 1 was quite large. More efforts are needed to accelerate the calculations while maintaining a reasonable level of accuracy and robustness. Fast fluid dynamics (FFD) could potentially be used to accelerate the transient airflow calculations [50–52], while the Markov chain model could significantly reduce the computing time for transient particle transport [53–55]. Second, in this study, the wiping method was used to obtain the quantitative particle deposition distribution with a resolution of 3 × 20 mm2. When a higher resolution is required, however, the measurement errors due to the wiping process will increase significantly. Therefore, it is worthwhile to develop novel methods for more detailed measurements of the distribution. The fluorescence spectroscopy method [56] and neutron activation analysis [57], with certain improvements, could be utilized in the future. Finally, the calculations in this study assumed that the target surface was smooth because the actual target surface in the experiment was polished to ensure a small roughness value. In real applications, however, the surfaces may not be smooth, and roughness has been proven to be an important factor in particle deposition [58,59]. Therefore, the influence of surface roughness on particle deposition distribution should be considered both experimentally and numerically. The enhanced soiling around a multi-slot diffuser can be solved in several ways. First, the proposed LES-Lagrangian model can be used to design new diffusers with reduced particle deposition. Computer-aided design with an accurate model can be a good alternative to trial-anderror prototype development, saving time and money. The design objective would be to minimize the particle deposition velocity while maintaining the supply air requirements, such as airflow uniformity, supply air magnitude and angle. Second, if the existing multi-slot diffusers cannot be replaced, remedial measures can be taken. For example, Timmer and Zeller [21] proposed drilling several holes near the ceiling induction outlets to reduce particle deposition. Surface polishing is another measure to reduce the roughness and thus the particle

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