Experimental study on deposition enhancement of ultrafine particles in a duct flow by riblets

Applied Thermal Engineering 147 (2019) 886–894

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Experimental study on deposition enhancement of ultrafine particles in a duct flow by riblets

T

H.H. Zhang, S.S. Nunayon, A.C.K. Lai

⁎

Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong

ARTICLE INFO

ABSTRACT

Keywords: Ultrafine particles Particle deposition Duct flow Enhanced deposition Riblets

High filtration for ultrafine particles (UFPs) has many potential energy-saving and environmental applications. In this study, riblet surfaces with different geometries were investigated for their enhanced UFPs deposition in duct flow conditions for the first time. Polydisperse sodium chloride (NaCl) particles as UFPs were used and tested in a wide range of Reynolds numbers, ranging from laminar to fully turbulent flow. The upstream and downstream size-resolved particle concentrations of the NaCl particles were measured. Experimental results show that deposition velocity increased with Reynolds numbers and decreased with particle size for both empty duct and duct furnished with riblet surfaces. Duct with riblets surface had the highest enhanced deposition velocity ratio for UFPs in the laminar regime, which could reach about 7.0 times for particles less than 20 nm, and about 4.8 times for particle size between 20 nm and 50 nm. The experimental results reveal that the friction factors of the duct with riblet surfaces were close to that of the empty duct in the turbulent flow, while higher pressure drop penalty was observed for riblet surfaces in the laminar flow. The performance index of riblet surfaces by combining enhanced UFPs deposition and high frictional drag was also evaluated. The results show that the highest performance ratio of riblets could be up to 4.0. In addition, the riblet surface with largest protrusion height generally give the best performance.

1. Introduction

concentration levels by only 34% [10]. For the MERV (Minimum efficiency reporting value) 6 filter, the removal efficiency to most UFPs is less than 10% [11]. The filtration efficiency of MERV 8 filter to 100 nm particle is very low [12]. To improve filtration of fine particles, fibrous filters such as the high-efficiency particulate air (HEPA) filters have been widely employed. However, they comprise very fine glass fibers with an average diameter between 0.5 and 5.0 µm, which are closely packed [13]. As a result, resistance against airflow is created in the form of excessively high-pressure drops. The pressure drop for a filter with a minimum efficiency reporting value (MERV) of 16 is 130% higher than that of one with a MERV of 8 [14]. Nevertheless, those high-efficiency fibrous filters are not currently installed in general premises due to high-pressure drops and their very high operation cost. For mechanically ventilated buildings, substantial energy is used to filter ventilation air to an acceptable level. The fan energy required to overcome this resistance accounts for 30% of an HVAC system’s average energy consumption [15]. To reduce the energy consumed by HVAC fans, other filtration capture mechanisms have been developed. Electret filters provide a low-pressure drop penalty and are suitable for removing UFPs. The major drawback is the deterioration of their performance due to the

Good indoor air quality has been shown to improve occupants’ health, work productivity and even a city’s economic competitiveness [1–3]. Ventilation air is needed to remove indoor pollutants, nonetheless, it can be seriously polluted with ultrafine particles (UFPs). They can penetrate indoors through ventilation systems [4]. UFPs are particulate matters with nanoscale sizes, which are less than 100 nm in diameter. They can be generated by many activities such as cooking, smoking, incense burning and vacuum cleaning [5,6]. Also, as particle size decreased, the UFPs deposition fraction would be increased during spontaneous breathing [7]. Recent scientific and toxicological evidence had shown the severe health effects of inhalation of UFPs [8,9]. Thus, it is necessary and important to use filter for removing UFPs from the air. Fibrous filters have a long history of use and they are the most commonly used filters for heating, ventilation, and air-conditioning (HVAC) systems. In practice, it can be categorized as low-efficiency, mediumefficiency, and high-efficiency grades. Low-efficiency filters are always used as pre-filters. Medium efficiency filters are used in most commercial buildings. Studies showed that an HVAC system in an office building with a medium grade filter reduced submicron particle ⁎

Corresponding author. E-mail address: [email protected] (A.C.K. Lai).

https://doi.org/10.1016/j.applthermaleng.2018.10.112 Received 26 January 2018; Received in revised form 18 October 2018; Accepted 24 October 2018 Available online 25 October 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 147 (2019) 886–894

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Nomenclature

Ci

Cup,i Cd,i Dh ERi LOi L Uave Vd,i f ΔP u s

s+

non-dimensional riblet spacing

Greek symbols

particle concentration difference (#/cm3) upstream particle concentration (#/cm3) downstream particle concentration (#/cm3) hydraulic diameter (m) enhanced deposition velocity ratio particle removal percentage (%) length of the surface concerned (m) average air velocity (m/s) deposition velocity (m/s) friction factor pressure drop (Pa) friction velocity of air (m/s) riblet spacing (m)

v

i

a

particle deposition performance ratio kinematic viscosity (m2/s) air density (kg/m3)

Subscripts i

particle bin or particle size group

Abbreviations UFPs

ultrafine particles

power efficiency were modeled. Riblet surfaces have been studied extensively and are well-known as a passive means for drag reduction for turbulent flows [31,32]. They have been rarely studied for enhanced heat transfer (EHT). Previous studies of riblets mainly focused on drag reduction. The mechanism responsible for the drag reduction may be related to the restriction of span-wise movement and the reduced turbulent intensity [33,34]. Due to the property of flow drag reduction, riblets have been applied successfully in wings and aircraft [35]. Those riblets are small protrusion heights submerged in viscous sublayer. But riblets with higher protrusion heights would inevitably increase flow drag. No studies have been conducted to investigate the enhancement of UFPs deposition by riblets in the duct air flow. In this work, riblet surface was selected to be one kind of roughness surfaces for enhancing UFPs deposition for duct flow with low to moderate high air velocity. Experiments were conducted to test three riblets with different geometries for the deposition enhancement of UFPs for the first time. Size-resolved UFPs concentration and pressure penalty in the duct airflow were measured under various air velocities, and performance of riblet surfaces was evaluated by combining the particle deposition and the pressure penalty. The objective of this pilot work is to investigate the effect of riblet surfaces under duct flow on the enhancement of UFPs deposition and to determine the filtration performance of riblets. It would potentially provide a solution for removing UFPs from the air and improving indoor air quality (IAQ) within mechanical ventilated/air-conditioned environments.

decay of electrostatic force as filtration proceeds [16] or when exposed to high relative humidity. Ion-assisted air filters are reportedly adequate for further enhancement of the coulombic force but with attendant relatively weak fiber polarization [17]. In fact, all fiber-type filters suffer one major drawback—a high pressure drop that increases over time which leads to a decrease in airflow rate. In view of this, it is obvious that the use of fibrous filters involves not only an initial cost but high maintenance and operation costs. Electrostatic precipitators are very efficient at coarse particle collection and are widely used for industrial emission removal, but their efficiency with UFPs is low [18]. Byproduct ozone emission is also a major health concern [19]. All available HVAC filters have their own limitations. To solve the dilemma of reducing energy as well as maintaining good indoor air quality, there is an urgent need for developing alternative filters. That said, though the direct benefit of studying energy-efficient high-efficiency particulate air filter is obvious, very few such studies can be found in the literature. It has been shown that particle deposition rate can be enhanced by rough surfaces [20–23]. One major reason that can be credited to this is that roughness of surfaces can increase particle deposition by providing places for particle impaction and by reducing the thickness of the viscous sublayer near the wall [23]. The first experimental data on spatial aerosol deposition on an obstructed duct was reported by Lai et al. [20,21]. They studied enhanced particle deposition with transverse ribs and pseudo-3D elements for ventilation ducts. Neutron activation analysis (NAA) was used to get aerosol particle deposition velocity. The particles tested were in the range of 0.7–7.1 µm. The enhanced deposition mechanism was inertia. The efficiency ratio of 1.37–1.89 and a pressure drop of 3.2 were reported. The results showed that the deposition velocity of ribbed surface can reach 7 times that of smooth surface. This increased roughness scale will enhance particle deposition rate [22]. In the previous study conducted by the authors [24], it was found that particle deposition velocity can be enhanced by twisted tape. Highest particle deposition velocity ratio was 3.3 times for particles sizes between 50 nm and 100 nm. Computational works also reported enhanced particle deposition for ribbed channels. Numerical investigations documented that square ribs performed five times better than other rib shapes [25]. The effects of rib spacing and height on particle deposition were also studied [26]. Results showed that a reduction in rib spacing increased enhancement of coarse particle deposition, whereas no marked difference was observed for rib heights. Compared with staggered rib surfaces, better performance on the enhancement of particle deposition can be observed for the surface ribs with aligned arrangement [27]. The effect of particle sizes [28], 90° square bend [29] and variable section ducts with various expanding or contracting ratios [30] on the particle deposition rate had also been studied. But these studies were all performed for particle sizes from 1 to 50 µm or bigger sizes. The results could be more informative if UFPs, pressure penalty and the equal

2. System design and methodology Three distinct types of longitudinal riblets were tested (Fig. 1). A wide range of Reynolds number was considered, ranging from 530 to 8010. Height [h], width [w], and pitch spacing [s] were used to describe the riblets and are shown in Fig. 1. The riblet plates were made of aluminum. A plane of 12.5 mm × 475 mm was fabricated for each riblet type (Fig. 2). A 15 mm × 15 mm × 2.48 m long square duct was designed and constructed. It was made entirely of transparent Perspex. Fig. 2 shows the experimental setup. Particle concentration was measured at upstream and downstream test points shown at locations “B” and “C”, respectively in Fig. 2. The distance between the two measurement points was 1.33 m. The units operated at various airspeed: 0.5 ms−1 (Re = 530), 1.2 ms−1 (Re = 1240), 2.3 ms−1 (Re = 2250), 4.0 ms−1 (Re = 4020), 6.0 ms−1 (Re = 6010), and 8.0 ms−1 (Re = 8010). The airstream velocity in the duct was measured with a portable anemometer (Kanomax A004) inserted through point C (see Fig. 2). The sensor of the anemometer was placed perpendicular to the airstream to ensure proper airspeed readings. The accuracy of the anemometer sensor was ± 3% of readings or 0.015 m/s whichever is greater. The 887

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Fig. 1. Three different riblet surfaces tested.

measurement was repeated for various airflow velocities during the experiment. A centrifugal fan with a variable-input voltage was used to induce the airflow in the ducts. Polydisperse solid particles were injected into the duct system at the fan mixing zone. The particles were produced by dissolving 0.5 g sodium chloride (NaCl) in 900 ml of deionized water, and compressed air was imparted on the solution by passing it through a 24-jet nebulizer (Collision Nebulizer, BGI). A scanning mobility particle sizer spectrometer system (Model 3080 TSI), consisting of a long differential mobility analyser, DMA (Model 3081, TSI) and a condensation particle counter, CPC (Model 3775, TSI), were used to measure the size-resolved particle concentration from 5.94 nm to 224.7 nm. The accuracy of particle concentration counted by CPC is ± 10% when the particle number concentration is lower than 5 × 104 particles/cm3. But for higher particle concentration, i.e. < 107 particles/cm3, the specified accuracy of CPC according to the manual of the manufacturer is ± 20%. To achieve a high accuracy, the particle concentrations measured in this work were less than 5 × 104 particles/cm3. SMPS has a definite advantage in measuring the concentration in bins, instead of total concentration. To facilitate analysis of the experimental results, the results were grouped into 5 bin classes: D < 20 nm, D = 20–50 nm, D = 50–100 nm, D = 100–150 nm and D > 150 nm.

By the nature of generation, the particles would carry electrostatic charges. The electrostatically enhanced deposition loss would interfere interpretation of results, particularly for the small duct size used in this work. Therefore, two measures were taken; a radioactive neutralizer was employed to remove the electrostatic charges on the testing particles by emitting beta particles and the conductive tubes were used for particle sampling. Finally, to evaluate the pressure drop for both empty duct and duct with riblet surface, the differential static pressure at upstream and downstream across the test section were measured, respectively by using an IAQ meter (Testo 480) at the pressure traps. Fig. 2 shows the measuring points “B” and “C.” The employed IAQ meter has internal piezoresistive sensor with the accuracy of 1% for the measuring of differential pressure between 0 Pa and 2500 Pa. 3. Experimental procedure Riblet plates (A, B and C) were put in a predetermined location between point B (upstream) and point C (downstream) inside the ductwork (see Fig. 2). A centrifugal fan speed was gradually increased and the anemometer reading monitored until the airstream velocity reached 0.5 ms−1. The NaCl suspension was nebulized and fed into the

Fig. 2. Experimental setup.

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ductwork system for 5 min before sampling to ensure the concentration output has been stabilized. The upstream concentration was scanned three times. The sampling tube was then inserted at the downstream position to scan the downstream aerosol concentration three times. To get reliable and credible measurements, the sampling tube was put back at the upstream position, and the procedure was repeated two more times. After one velocity setting was finished, the voltage was adjusted to another level and the procedure was repeated. This sampling procedure was applied for both the empty duct and duct fitted with different riblet surfaces. The entire measurements were repeated at least three times. 4. Data reduction In the present work, the air with UFPs flows through the empty duct and distinct types of riblets. The concentration difference of the aerosols for size bin i equals

Ci = Cup, i

Cd, i

(1)

Fig. 3. Deposition velocity of different particle sizes for the empty duct.

where Ci is the concentration difference of bin i, and Cup,i and Cd,i are the concentrations of bin i upstream and downstream, respectively. The particle removal percentage (LOi) for each bin i can be expressed as

LOi =

Ci × 100% Cup, i

deposition enhancement. Finally, the friction velocity, u , was calculated by [25],

u = Uave f /2

(2)

The uncertainties of these parameters were estimated and shown in the Appendix.

Particle deposition velocity was used to quantify the deposition loss. In this work, LOi was measured by Eq. (3) and it was related to the deposition velocity (Vd,i) by the following expression [36].

LOi = 1

[exp( 4LVd, i/ Dh Uave )]

5. Results and discussions

(3)

5.1. Particle deposition velocity for the empty duct

where L is the length of the surface concerned, Dh is the hydraulic diameter, and Uave is the average air velocity. After calculating deposition velocity of the individual bin, deposition velocity for each group was determined by averaging the Vd,i for those bins within the group. The enhanced deposition velocity ratio (ERi) was calculated as the ratio of the particles deposition velocity by ribleted surface to the particles deposition by the empty duct system. It is given as

ERi =

Vd, i (riblet ) Vd, i (empty )

Fig. 3 illustrates the deposition velocity, Vd of various groups of particle size for the empty duct. As indicated in the figure, the deposition velocity of each bin in empty duct increases with Reynolds number. This is because the deposition of UFPs is influenced mainly by turbulent diffusion which will be increased with Reynolds number, while the effect of inertia, primarily affecting the deposition of micrometer size particles, is negligible for UFPs [36]. With the increase of Reynolds number from 530 to 8010, the deposition velocity in empty duct increased 7, 24, 41, 28 and 35 times for particulate matters, less than 20 nm, 20–50 nm, 50–100 nm, 100–150 nm and lager than 150 nm respectively. From Fig. 3, the deposition velocity also increased as the particle size decreases. This might be explained by the fact that the Brownian diffusion of smaller particles is stronger than that of bigger particles [38]. Generally, our experimental results of deposition velocities for various particle bins of UFPs in empty duct varied in the range of 1.94 × 10−5–1.28 × 10−3, which are similar to the experimental and theoretical results of [36] for 10–40 nm size of particles when tested Reynolds number was less than 9000.

(4)

where Vd,i(riblet) and Vd,i(empty) are the particle deposition velocity for ducts with riblet and empty ducts, respectively. The fanning friction factor, f, was calculated from the pressure drop, ΔP, across the upstream and downstream of the air duct [37]. In this study, f(riblet) and f(empty) are the friction factors for ducts with riblets and empty ducts, respectively. The enhancement of particle deposition can be achieved by the increase of roughness [20,21]. Riblet surface as one kind of roughness surfaces may also enhance the particle deposition. But at the same time more flow drag for the riblet surface would be observed, compared with that of smooth surfaces. In order to evaluate the performance of different riblets by taking account of effects of the particle deposition enhancement and pressure penalty together, the particle deposition performance ratio (η) is defined, which is the ratio of the enhanced deposition velocity ratio to the friction factor ratio under the constant fan power [24]: i

=

5.2. Particle deposition velocity by riblets In this work, three riblets were employed to get the deposition characteristics of UFPs for riblet’s surface in the duct. For the duct furnished with the riblets, the trend of deposition velocity was consistent with that of the empty duct. Fig. 4 shows the variation of deposition velocities of various particle size groups in the same duct fitted with different riblets. The deposition velocities increased with Reynolds number, while deposition velocities decreased as particle size increases. Generally, at lowest Reynolds number the velocity of particle deposition had the minimum value for the three riblets. With the increase of Reynolds number from 530 to 8010, the highest increase rates in

ERi f(riblet ) f(empty)

(6)

(5)

Performance ratio is defined as an evaluation parameter, which represents the overall or comprehensive efficiency for particle

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Fig. 4. Deposition velocity of different particle sizes for riblets, (a) Riblet A, (b) Riblet B, (c) Riblet C.

deposition velocity were found to be 29 times and 86 times for particle sizes between 50 nm and 100 nm for duct fitted with riblet A and B, respectively. While for riblet C, when Re increased from 530 to 8010, the highest increase rate in deposition velocity achieved was up to 60 times for particles larger than 150 nm.

Fig. 5. Enhanced deposition velocity ratio for riblets for different Reynolds number, (a) Riblet A, (b) Riblet B, (c) Riblet C.

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Fig. 6. Variation of friction factor with Reynolds number.

In addition, the deposition velocity of riblets is obviously higher than that of the empty duct. This means that the enhancement of particle deposition by riblets is a possibility. Fig. 5 presents the variation of enhanced deposition velocity ratio with Reynolds number for the duct furnished with different riblets. It reveals that the ratios of enhanced deposition velocity for tested riblets were mostly higher than 1.0, which validated UFPs’ deposition enhancement of the riblet surface in the duct. Fig. 5 also shows that the highest ratio of deposition velocity for three riblets happened all in the case of laminar flow. For particles less than 20 nm in the case of riblet A and riblet B, the highest deposition velocities at Re = 1240 and Re = 2250 can reach 7 times and 2.6 times, respectively than that of the empty duct. The result of riblet C peaks at 4.8 times for particle size between 20 nm and 50 nm for Re = 530. 5.3. Friction factor As shown in Fig. 6, the experimental results of friction factor of the three riblets inserted into ventilation duct were compared with the empty ventilation duct. Interestingly, no considerate increase was observed for all riblets. Like the friction factor in the empty duct, the friction factors for the three different riblets almost maintained a stable trend with increasing Reynolds number in turbulence flow. The riblet surfaces such as sharkskin riblets or triangular riblets have been investigated as a passive means of drag reduction and the enhancement of heat transfer [39,40]. The mechanism responsible for the drag reduction may be attributable to the restriction of spanwise movement and reduced turbulent intensity [41]. It is worthy to note that the non-dimensional riblet spacing is defined as s+ (= su / ) , where ν is the kinematic viscosity of air. For all tested riblets in our study, s+ was found larger than 30 in the turbulent flow, not within the drag-reducing regime, s+ < 30, of triangular riblet surfaces from others work [39]. When the s+ is greater than 30, riblet surface can increase the pressure penalty compared with empty duct, while increasing particle deposition occurs. This may be due to the fact that the riblet surface could be considered as rough surface at the drag-increasing regime (s+ > 30%) of riblets. In Fig. 6, only a slight difference in friction factor between empty duct and duct fitted with riblets was observed in the turbulent flow, while bigger drag penalty for riblets was observed in the laminar flow. This might indicate that the riblet surface is ineffective in reducing pressure penalty in the laminar regime, which is consistent with the result of direct numerical simulations over riblets [40].

Fig. 7. Variation of particle performance ratio for riblets with Reynolds number, (a) Riblet A, (b) Riblet B, (c) Riblet C.

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5.4. Performance evaluation

Laminar and turbulent flow conditions were tested with the wide range of Reynolds numbers from 530 to 8010. For empty air duct, due to the effects of both turbulent diffusion and Brownian diffusion, the deposition velocity of UFPs increased with Reynolds numbers (impact of turbulent diffusion) and inversely with particle sizes (impact of Brownian diffusion). For UFPs, these two diffusion rates are the dominant loss or deposition mechanisms. The duct with riblet surfaces achieved higher deposition velocity than empty duct for UFPs. Intuitively, any rough surfaces would add extra pressure penalty. Meanwhile, the pressure penalties for all tested riblet surfaces were almost close to that of the smooth duct in turbulent flow. The performance ratio was also evaluated. The highest performance ratio for riblet surface could be up to 4.0. Since the highest performance was achieved at low Re, if the flow regime is carefully controlled, the riblet surface has immense potential for enhancing deposition of UFPs.

Compared with empty or smooth duct, the advantage of duct fitted with riblets is the enhancement of particle deposition. But the flow drag would (although slightly) be increased by riblet surfaces. Therefore, both effects need to be considered simultaneously for evaluating the overall or integrated performance of riblets. As mentioned the definition of performance ratios in data reduction, to evaluate the riblets’ performance, performance ratios for riblets were computed, as shown in Fig. 7. Riblets A, B, and C achieved the highest performance ratios of nearly 4.0, 2.0 and 3.8, respectively. It is interesting to observe that riblet A with highest protrusion height generally gives the best results. The particles with high relaxation time with inertia impaction is one of loss mechanisms, and protrusion height is very important. 6. Conclusions Gaining more knowledge on deposition for ultrafine particle has many applications, not only for the filtration of particles, but also for saving energy in HVAC system. In this work, riblets were proposed to enhance the deposition of UFPs in the air duct for the first time. Polydisperse solid particles were employed as UFPs. Three different riblet surfaces were tested for particle deposition in a duct flow.

Acknowledgement The research described in this study was fully supported by a General Research Fund from the Research Grants Council of Hong Kong Special Administrative Region of China [CityU 11210015] and a grant from Natural Science Foundation China [51378447].

Appendix. Uncertainty analysis Based on the Kline and McClintock's method [42], the uncertainty analysis of the experimental results is performed as shown: n

f= j=1

f xj xj

2

(A1)

where f is the given function of several independent variables (xj j = 1 to n); δxj is the absolute error for the variable xj. The measured parameters are air velocity, duct length, duct width, duct height, tested section length, pressure drop across test section and particle concentration. They are all showed in the Table A.1. Table A.1 Values of measured parameters Measured parameter

Value

Duct width Duct height Length of tested section Air velocity Particle concentration Pressure drop across the test section

W = 15 mm H = 15 mm L = 1330 mm V = 0.5–8.0 m/s 104–5 × 104/cm3 10–150 Pa

The calculated parameters are hydraulic diameter of the duct, Reynolds number, friction factor, particle concentration difference, particle deposition velocity, enhanced deposition velocity ratio and particle deposition performance ratio. Uncertainties of these calculated parameters are estimated as shown in the following. A.1. Hydraulic diameter of the duct, Dh

Dh =

2WH = 15 mm (W + H )

(A2) (A3)

W = H = 0.05 mm

Dh =

Dh W W

2

+

Dh H H

2

=

(0.5 × 0.05) 2 + (0.5 × 0.05)2 = 0.035 mm

(A4)

The relative uncertainty of hydraulic diameter, Dh

Dh × 100% = 0.2% Dh

(A5)

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A.2. Reynolds number, Re

Re =

Uave Dh v

(A6)

The relative uncertainty of air velocity

Re = Re

2

Uave Uave

Dh Dh

+

Re × 100% = Re

( Uave ) Uave

of a portable anemometer (Kanomax A004), given by the manufacturer, is 3%. Thus,

2

(A7)

(3%) 2 + (0.2%)2 = 3%

(A8)

A.3. Friction factor, f The fanning friction factor (f), is expressed as [37]:

2 PDh 2 a Uave L

f=

(A9)

The uncertainty of pressure drop ( P ), is 1% of pressure in Pascal. Thus,

f = f

P P

2

f × 100% = f

2

Dh Dh

+

Uave Uave

+

2

+

Uave Uave

2

+

(1%)2 + (0.2%) 2 + (3%) 2 + (3%) 2 +

L L

2

0.05 1330

2

(A10)

= 4.3%

(A11)

A.4. Particle concentration difference, Ci

Ci = Cup, i

(A12)

Cd, i

The relative uncertainty of particle concentration measured by condensation particle counter (Model 3775, TSI) is 10%. Thus,

Ci = Ci

(10%) 2 + (10%)2 = 14.1%

(A13)

A.5. Particle deposition velocity, Vd,i The relative uncertainty of particle removal percentage (LOi) is expressed as:

LOi = LOi

(10%) 2 + (10%)2 = 14.1%

(A14)

Then particle deposition velocity (Vd,i) can be expressed as:

Dh Uave ln(1 4L

Vd, i =

ln(1 ln(1

(

LOi ) = LOi )

Vd, i = Vd, i

Dh Dh

LOi ) ln(1 LOi) LOi

ln(1 2

+

(A15)

Uave Uave

LOi

)

2

(A16)

LOi ) 2

+

ln(1 ln(1

LOi ) LOi )

2

+

L L

2

(A17)

Therefore, the relative uncertainties of deposition velocity (Vd,i) for empty duct are between 14.49% and 15.12%. The relative uncertainties of deposition velocity (Vd,i) range from 14.49% to 19.55%, 14.50% to 15.84% and 14.44% to 16.56% for riblet A, B and C respectively. A.6. Enhanced deposition velocity ratio, ERi

ERi =

Vd, i (riblet ) Vd, i (empty )

ERi = ERi

Vd, i (riblet ) Vd, i (riblet )

(A18) 2

+

Vd, i (empty)

2

Vd, i (empty)

(A19)

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The relative uncertainties of enhanced deposition velocity ratio (ERi) range from 20.51% to 24.66%, 20.50% to 21.84% and 20.52% to 22.42% for riblet A, B and C respectively. A.7. Particle deposition performance ratio, η

=

i

ERi f(riblet )

(A20)

f(empty)

i

ERi ERi

2

=

ERi ERi

2

=

i

i i

+

f(riblet ) f(riblet )

2

++

f(empty )

2

f(empty )

(A21)

+ (4.3%) 2 + + (4.3%)2

(A22)

The relative uncertainties of performance ratio (η) range from 21.40% to 25.40%, 21.38% to 22.66% and 21.40% to 23.23% for riblet A, B and C respectively.

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