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Analytical Prediction Model for Indoor Particle Deposition onto Ocular Surface
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 88 (2016) 709 – 713
CUE2015-Applied Energy Symposium and Summit 2015: Low carbon cities and urban energy systems
Analytical Prediction Model for Indoor Particle Deposition onto Ocular Surface Zhang Yang, Li Nianping*, Wang Chen, Zeng Jing School of Civil Engineering , HuNan University, South LuShan road number 2, ChangSha and 410082, China
Abstract This paper was based on the definition of particle deposition velocity. By analysis the deposition mechanisms of particle in concentration boundary layer, the paper deduced an analytical expression of differential equation about dimensionless deposition velocity onto ocular surface. Then the paper adopted a series of reasonable approximation formula to simplify the expression of dimensionless deposition velocity. The rationality and the accuracy of the prediction model were verified by experimental data in a reference paper. It was testified that the deposition velocity onto the ocular surface firstly decreases and then increases with the increase of the particle diameters when under low friction velocity. The deposition velocity continuously increases with the increase of the particle diameters when under relatively high friction velocity. The model could contribute to low carbon city, energy conservation and emissions reduction in theory. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-reviewofunder responsibility of CUE Peer-review under responsibility the organizing committee of CUE 2015
Keywords: Low carbon; energy saving; prediction model; deposition velocity; particle
1. Introduction One of the characteristics of Low carbon city is that the proportion of fossil fuels account for 50% below in urban energy structure [1]. Controlling atmospheric pollutants is one of the important measures to implement low carbon city. There is a concern of more than 100 kinds of atmospheric pollutants in the city, which can be divided into two types: granular pollutants and gaseous pollutants [2]. Particles and CO2 produced by burning fossil fuels reduce the ground radiation effectively and strengthen the urban heat island effect, leading to air conditioning energy consumption increased in summer. Therefore, the combustion of coal is not conducive to low carbon city development, also it increases the energy consumption of urban energy system. Effects of indoor particles onto ocular surface not only depend on the concentration of the particle size, but also closely relate to settlement of particles. When in a certain concentration of indoor particles, the
* Corresponding author. Tel.: 13508483115; fax: 0731-88823000. E-mail address:[email protected]
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of CUE 2015 doi:10.1016/j.egypro.2016.06.048
710
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
settlement of particles is proportional to deposition velocity. Fu ZY et al. proposed the analytical method of the particle deposition velocity in air ducts, but the model did not consider the temperature difference between the air in pipe and the duct surface [3]. Gudmundsson et al. put dummy model in wind tunnel, and measured the deposition velocity of some diameter particles onto ocular surface under two turbulence intensities [4]. Schneider et al. proposed the semi-empirical formula of deposition velocity and it was almost consistent with wind tunnel experiment data [5]. Schneider et al. made a combination of multiple factors, then put forward probability model to predict deposition velocity onto ocular surface [6]. This paper was based on the definition of particle deposition velocity, and proposed a new analytical prediction model for indoor particle deposition onto ocular surface. Nomenclature J
settlement of particle
D
Brownian diffusion coefficient turbulent diffusion coefficient
C
concentration of particle
vthermo
thermophoretic velocity
Y
distance from ocular surface
Vd
deposition velocity
Sc
Schmidt number
dp
diameter of particle thickness of concentration boundary layer
T∞
environmental temperature
Ts
surface temperature
K
ratio of the thermal conductivity of air and the particle
u
*
friction velocity
2. Prediction model 2.1. Differential equation Supposed that concentration boundary layer of ocular surface had no source and collection of particle, so settlement of particles is constant: (1) The definition of deposition velocity [8] is: (2)
711
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
For convenience, this paper nondimensionalized friction velocity, viscosity of air, particle concentration of mainstream and air temperature. By bringing all the dimensionless parameters into the definition equation of deposition velocity, the paper got the following differential equation: (3) When y+= y0+ then C+=0 and when y+=4.3 then C+=1, and y0= dp /2. 2.2. Expressions of differential equation 2.2.1. Brownian diffusion Studies have shown that the thickness of dimensionless concentration boundary layer is a linear function of particle diameter. Thickness of boundary layer can be approximately described with Schmidt number Sc [3]: (4) When , the concentration boundary layer of particle is . When C+ equals 0.9, thickness of concentration boundary layer decreases sharply with the increasing of particles diameter. So the paper induced: (5) 2.2.2. Turbulent diffusion When the dimensionless relaxation time of particles satisfies <0.1, the ratio between turbulent diffusion coefficient and turbulent viscosity coefficient approaches to 1[10]. Dimensionless relaxation time conformed to 0.05 in this paper, so it was identified that turbulent diffusion coefficient of particle equaled air turbulence viscosity coefficient of indoor air. Studies have shown that turbulence viscosity coefficient of particles increased sharply with the increasing of the distance from the deposited wall. This paper selected the result of direct numerical simulation [12]: (6) 2.2.3. Thermophoresis The temperature of ocular surface is generally higher than indoor air. Temperature difference results in thermophoresis speed [13]: (7) 2.3. Solution of prediction model By putting formulas (5) (6) and (7) into the analytical expressions for dimensionless deposition velocity and solving the first order linear non-homogeneous differential equation, this paper work out the dimensionless deposition velocity Vd+: (8) (9)
712
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
(10) Thickness of concentration boundary layer when dp=0.1μm is approximately equal to y+=4.3, and for dp =10μm thickness of concentration boundary layer is y+=0.01[7], so this paper assumed that when y+=4.3, the concentration of particles is equal to the concentration of the mainstream C∞. Studies show that even if particle size is 0.01μm, thickness of concentration boundary layer is existed inside the viscous sublayer. Therefore, the differential equation of dimensionless deposition velocity adopt y+=4.3 as the upper limit of integral for the concentration boundary layer in the paper. 3. Model verification This paper solved the model in experimental condition, which was the same to T. Schneider et al. [6], then compared predicted value with experimental value. Table1. Prediction value and experimental data when u*=0.015m/s Number
Diameter˄μm˅
Deposition Velocity Vd˄m/s˅ Experiment Value
Predicted Value
0.1
1.0 u 10-6
2.94 u 10-6
2
1
4.5 u 10
-7
1.68 u 10-6
3
6
3.2 u 10-6
3.94 u 10-6
10
8.7 u 10
-6
4.59 u 10-6
5 20 9.3 u 10 Table2. Prediction value and experimental data when u*=0.15m/s
-6
3.56 u 10-6
1
4
Number 1 2 3 4 5
Diameter˄μm˅ 0.1 1 6 10 20
Deposition Velocity Vd˄m/s˅ Experiment Value Predicted Value 1.8 u 10-5 2.94 u 10-5 7.8 u 10-5 4.76 u 10-5 3.5 u 10-4 3.99 u 10-5 8.9 u 10-4 7.75 u 10-5 -4 9.6 u 10 8.34 u 10-5
Tables shown that most of the velocity gaps between predicted and experimental results were within the same magnitude, and the predicted results were fitted with T. Schneider et al. experimental values well. In order to verify the validity of the predicted model further, this paper used the model to predict deposition velocities in three friction conditions: u*=0.2m/s, u*=0.25m/s, u*=0.3m/s.
Fig.1. The relationship whit dimensionless deposition velocity and particle
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
When the friction velocity is relatively high (u*≥0.2m/s), deposition velocity continuously increase with the increasing of the particle diameters. The deposition velocity onto the ocular surface constantly increases with the increase of the friction velocity when at the same particle diameters. 4. Conclusion The analytical prediction model proposed by this article has clear physical interpretation and it could effectively avoid the random error caused by the probability model, which was different from the previous experienced and the semi-empirical formulas. The paper adopted a series of reasonable approximation formula to simplify the expression of dimensionless deposition velocity. Deposition velocity onto the ocular surface firstly decreases and then increases with the increase of the particle diameters when under low friction velocity. Deposition velocity continuously increases with the increase of the particle diameters when under relatively high friction velocity. When diameter of particle is a constant, the higher particle friction velocity is the faster the deposition velocity is. The model could contribute to low carbon city, energy conservation and emissions reduction in theory. Acknowledgement I would like to express my gratitude to all those who helped me during the writing of this thesis.This st udy was sponsored bythe National Natural Science Foundation of China (No.51178169). Reference [1] Long WD, Bai W, Liang H, Fan R, Zhang GJ. Low carbon urban form and energy vision of the city. Building Science, 2008, 35(2). [2] Long WD, Bai W, Liang H, Fan R. Low carbon energy system of the city. HV&AC, 2009, 39(8). [3] Fu ZR, Li NP, Wang HQ. Analytical predition model for particle deposition in ventilation ducts. Journal of Hunan University (Natural Sciences), 2008, 35(2). [4] Gudmundsson, A., Schneider, T.Bohgard, M., Vinzents, P. and Akselsson,K.R.(1997) Deposition of airborne particles onto the human eye: wind tunnel studies of the deposition velocity onto the eyes of a mannequin, J. Aerosol Sci., 28, 1085–1100. [5] Schneider, T., Bohgard, M. and Gudmundsson, A. A semiempirical model for particle deposition onto facial skin and eyes . Role of air-currents and electric fields, J. Aerosol Sci.,1994( 25): 583–593. [6] Schneider, T., Bohgard, M. Airborne particle deposition onto the ocular surface. Indoor Air, 2005(15): 215–219. [7] Alvin C.K. Lai and William W. Nazaroff. Modeling indoor particle deposition from turbulent flow onto smooth surfaces. J. Aerosol Sci. 2000, 31(4):463—476. [8] CHEN F Z, LAI A. An Euhrian model for particle deposition under electrostatic and turbulent conditions[J]. Joumal of Aerosol Science, 2004, 35(1):47—62ˊ [9] Schlichting, H. (1979) Boundary layer theory, 7th Edition. McGraw-Hill, New York. [10] Uijttewaal W S JˈOliemans R V AˊParticle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flowsˊPhysics Fluids,1996,8(1 0)˖2590—2604 [11] Hinds W CˊAerosol technologyˊNew York˖John Wiley&Sons, 1982(2);45; 274-280; 38-42; 128-131; 123-124. [12] Kim, J., Moin, P. and Moser, R. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 1987, (177): 133-166. [13] Schneider, T., Kildeso, J. and Breum, N.O. A two compartment model for determining the contribution of sources, surface deposition and resuspension to air and surface dust concentration levels in occupied rooms, Build. Environ, 1999, (34): 583–595.
713
ScienceDirect Energy Procedia 88 (2016) 709 – 713
CUE2015-Applied Energy Symposium and Summit 2015: Low carbon cities and urban energy systems
Analytical Prediction Model for Indoor Particle Deposition onto Ocular Surface Zhang Yang, Li Nianping*, Wang Chen, Zeng Jing School of Civil Engineering , HuNan University, South LuShan road number 2, ChangSha and 410082, China
Abstract This paper was based on the definition of particle deposition velocity. By analysis the deposition mechanisms of particle in concentration boundary layer, the paper deduced an analytical expression of differential equation about dimensionless deposition velocity onto ocular surface. Then the paper adopted a series of reasonable approximation formula to simplify the expression of dimensionless deposition velocity. The rationality and the accuracy of the prediction model were verified by experimental data in a reference paper. It was testified that the deposition velocity onto the ocular surface firstly decreases and then increases with the increase of the particle diameters when under low friction velocity. The deposition velocity continuously increases with the increase of the particle diameters when under relatively high friction velocity. The model could contribute to low carbon city, energy conservation and emissions reduction in theory. © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-reviewofunder responsibility of CUE Peer-review under responsibility the organizing committee of CUE 2015
Keywords: Low carbon; energy saving; prediction model; deposition velocity; particle
1. Introduction One of the characteristics of Low carbon city is that the proportion of fossil fuels account for 50% below in urban energy structure [1]. Controlling atmospheric pollutants is one of the important measures to implement low carbon city. There is a concern of more than 100 kinds of atmospheric pollutants in the city, which can be divided into two types: granular pollutants and gaseous pollutants [2]. Particles and CO2 produced by burning fossil fuels reduce the ground radiation effectively and strengthen the urban heat island effect, leading to air conditioning energy consumption increased in summer. Therefore, the combustion of coal is not conducive to low carbon city development, also it increases the energy consumption of urban energy system. Effects of indoor particles onto ocular surface not only depend on the concentration of the particle size, but also closely relate to settlement of particles. When in a certain concentration of indoor particles, the
* Corresponding author. Tel.: 13508483115; fax: 0731-88823000. E-mail address:[email protected]
1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of CUE 2015 doi:10.1016/j.egypro.2016.06.048
710
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
settlement of particles is proportional to deposition velocity. Fu ZY et al. proposed the analytical method of the particle deposition velocity in air ducts, but the model did not consider the temperature difference between the air in pipe and the duct surface [3]. Gudmundsson et al. put dummy model in wind tunnel, and measured the deposition velocity of some diameter particles onto ocular surface under two turbulence intensities [4]. Schneider et al. proposed the semi-empirical formula of deposition velocity and it was almost consistent with wind tunnel experiment data [5]. Schneider et al. made a combination of multiple factors, then put forward probability model to predict deposition velocity onto ocular surface [6]. This paper was based on the definition of particle deposition velocity, and proposed a new analytical prediction model for indoor particle deposition onto ocular surface. Nomenclature J
settlement of particle
D
Brownian diffusion coefficient turbulent diffusion coefficient
C
concentration of particle
vthermo
thermophoretic velocity
Y
distance from ocular surface
Vd
deposition velocity
Sc
Schmidt number
dp
diameter of particle thickness of concentration boundary layer
T∞
environmental temperature
Ts
surface temperature
K
ratio of the thermal conductivity of air and the particle
u
*
friction velocity
2. Prediction model 2.1. Differential equation Supposed that concentration boundary layer of ocular surface had no source and collection of particle, so settlement of particles is constant: (1) The definition of deposition velocity [8] is: (2)
711
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
For convenience, this paper nondimensionalized friction velocity, viscosity of air, particle concentration of mainstream and air temperature. By bringing all the dimensionless parameters into the definition equation of deposition velocity, the paper got the following differential equation: (3) When y+= y0+ then C+=0 and when y+=4.3 then C+=1, and y0= dp /2. 2.2. Expressions of differential equation 2.2.1. Brownian diffusion Studies have shown that the thickness of dimensionless concentration boundary layer is a linear function of particle diameter. Thickness of boundary layer can be approximately described with Schmidt number Sc [3]: (4) When , the concentration boundary layer of particle is . When C+ equals 0.9, thickness of concentration boundary layer decreases sharply with the increasing of particles diameter. So the paper induced: (5) 2.2.2. Turbulent diffusion When the dimensionless relaxation time of particles satisfies <0.1, the ratio between turbulent diffusion coefficient and turbulent viscosity coefficient approaches to 1[10]. Dimensionless relaxation time conformed to 0.05 in this paper, so it was identified that turbulent diffusion coefficient of particle equaled air turbulence viscosity coefficient of indoor air. Studies have shown that turbulence viscosity coefficient of particles increased sharply with the increasing of the distance from the deposited wall. This paper selected the result of direct numerical simulation [12]: (6) 2.2.3. Thermophoresis The temperature of ocular surface is generally higher than indoor air. Temperature difference results in thermophoresis speed [13]: (7) 2.3. Solution of prediction model By putting formulas (5) (6) and (7) into the analytical expressions for dimensionless deposition velocity and solving the first order linear non-homogeneous differential equation, this paper work out the dimensionless deposition velocity Vd+: (8) (9)
712
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
(10) Thickness of concentration boundary layer when dp=0.1μm is approximately equal to y+=4.3, and for dp =10μm thickness of concentration boundary layer is y+=0.01[7], so this paper assumed that when y+=4.3, the concentration of particles is equal to the concentration of the mainstream C∞. Studies show that even if particle size is 0.01μm, thickness of concentration boundary layer is existed inside the viscous sublayer. Therefore, the differential equation of dimensionless deposition velocity adopt y+=4.3 as the upper limit of integral for the concentration boundary layer in the paper. 3. Model verification This paper solved the model in experimental condition, which was the same to T. Schneider et al. [6], then compared predicted value with experimental value. Table1. Prediction value and experimental data when u*=0.015m/s Number
Diameter˄μm˅
Deposition Velocity Vd˄m/s˅ Experiment Value
Predicted Value
0.1
1.0 u 10-6
2.94 u 10-6
2
1
4.5 u 10
-7
1.68 u 10-6
3
6
3.2 u 10-6
3.94 u 10-6
10
8.7 u 10
-6
4.59 u 10-6
5 20 9.3 u 10 Table2. Prediction value and experimental data when u*=0.15m/s
-6
3.56 u 10-6
1
4
Number 1 2 3 4 5
Diameter˄μm˅ 0.1 1 6 10 20
Deposition Velocity Vd˄m/s˅ Experiment Value Predicted Value 1.8 u 10-5 2.94 u 10-5 7.8 u 10-5 4.76 u 10-5 3.5 u 10-4 3.99 u 10-5 8.9 u 10-4 7.75 u 10-5 -4 9.6 u 10 8.34 u 10-5
Tables shown that most of the velocity gaps between predicted and experimental results were within the same magnitude, and the predicted results were fitted with T. Schneider et al. experimental values well. In order to verify the validity of the predicted model further, this paper used the model to predict deposition velocities in three friction conditions: u*=0.2m/s, u*=0.25m/s, u*=0.3m/s.
Fig.1. The relationship whit dimensionless deposition velocity and particle
Zhang Yang et al. / Energy Procedia 88 (2016) 709 – 713
When the friction velocity is relatively high (u*≥0.2m/s), deposition velocity continuously increase with the increasing of the particle diameters. The deposition velocity onto the ocular surface constantly increases with the increase of the friction velocity when at the same particle diameters. 4. Conclusion The analytical prediction model proposed by this article has clear physical interpretation and it could effectively avoid the random error caused by the probability model, which was different from the previous experienced and the semi-empirical formulas. The paper adopted a series of reasonable approximation formula to simplify the expression of dimensionless deposition velocity. Deposition velocity onto the ocular surface firstly decreases and then increases with the increase of the particle diameters when under low friction velocity. Deposition velocity continuously increases with the increase of the particle diameters when under relatively high friction velocity. When diameter of particle is a constant, the higher particle friction velocity is the faster the deposition velocity is. The model could contribute to low carbon city, energy conservation and emissions reduction in theory. Acknowledgement I would like to express my gratitude to all those who helped me during the writing of this thesis.This st udy was sponsored bythe National Natural Science Foundation of China (No.51178169). Reference [1] Long WD, Bai W, Liang H, Fan R, Zhang GJ. Low carbon urban form and energy vision of the city. Building Science, 2008, 35(2). [2] Long WD, Bai W, Liang H, Fan R. Low carbon energy system of the city. HV&AC, 2009, 39(8). [3] Fu ZR, Li NP, Wang HQ. Analytical predition model for particle deposition in ventilation ducts. Journal of Hunan University (Natural Sciences), 2008, 35(2). [4] Gudmundsson, A., Schneider, T.Bohgard, M., Vinzents, P. and Akselsson,K.R.(1997) Deposition of airborne particles onto the human eye: wind tunnel studies of the deposition velocity onto the eyes of a mannequin, J. Aerosol Sci., 28, 1085–1100. [5] Schneider, T., Bohgard, M. and Gudmundsson, A. A semiempirical model for particle deposition onto facial skin and eyes . Role of air-currents and electric fields, J. Aerosol Sci.,1994( 25): 583–593. [6] Schneider, T., Bohgard, M. Airborne particle deposition onto the ocular surface. Indoor Air, 2005(15): 215–219. [7] Alvin C.K. Lai and William W. Nazaroff. Modeling indoor particle deposition from turbulent flow onto smooth surfaces. J. Aerosol Sci. 2000, 31(4):463—476. [8] CHEN F Z, LAI A. An Euhrian model for particle deposition under electrostatic and turbulent conditions[J]. Joumal of Aerosol Science, 2004, 35(1):47—62ˊ [9] Schlichting, H. (1979) Boundary layer theory, 7th Edition. McGraw-Hill, New York. [10] Uijttewaal W S JˈOliemans R V AˊParticle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flowsˊPhysics Fluids,1996,8(1 0)˖2590—2604 [11] Hinds W CˊAerosol technologyˊNew York˖John Wiley&Sons, 1982(2);45; 274-280; 38-42; 128-131; 123-124. [12] Kim, J., Moin, P. and Moser, R. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 1987, (177): 133-166. [13] Schneider, T., Kildeso, J. and Breum, N.O. A two compartment model for determining the contribution of sources, surface deposition and resuspension to air and surface dust concentration levels in occupied rooms, Build. Environ, 1999, (34): 583–595.
713