CFPD Simulation of Radioactive Particle Deposition in Lungs

Transcription

1 CFPD Smulaton of Radoactve Partcle Deposton n Lungs Ayhan Ylmazer*, Ceml Kocar, Ismal Sercan Özer, Cem Gündüzalp *Hacettepe Unversty, Eng. Fac., Nuclear Eng. Dept., 06800, Beytepe, Ankara, Turkey ylmazer@hacettepe.edu.tr, ckocar@hacettepe.edu.tr, sercanozer@gmal.com, cemgunduzlap@gmal.com ABSTRACT In ths study, we nvestgate local deposton of aerosol partcles n bronchal system. Models are formed wth the assumpton of three-stage bfurcaton of broncha and the computatonal grd s consttuted usng GAMBIT software of computatonal flud dynamcs code FLUENT. Calculatons are carred out for a varety of flow models avalable n FLUENT and for dfferent partcle ntake flow rates and partcle dameters. It s shown that k ω and low Reynolds number k models of FLUENT such as AB, AKN and CHC produce results whch are n perfect agreement among themselves and wth the lterature for partcle deposton computatons. It s also shown that standard k model s not sutable for analysng aerosols deposton n human respratory system. Consderng the fact that the dose dstrbuton due to the deposted partcles n lungs rather than ts average value s more crucal, t s demonstrated n ths work that computatonal flud partcle dynamcs CFPD smulatons are very convenent tools to estmate local depostons of radoactve aerosols. Based on the deposton models presented n the current study, local dose dstrbuton n lungs due to radoactve aerosol partcles ntake could be determned as a further step. 1 INTRODUCTION Smulaton of human respratory system s very dffcult to determne local depostons. Therefore, such nformaton has been nevtably tred to obtan from valdated computatonal flud-partcle dynamcs (CFPD) smulatons whch provde a non-nvasve, accurate, and costeffectve means. Nevertheless, presently CFPD analyses are restrcted to segments or regons of the respratory system [1]. Hence, global lung deposton models [-3], relyng on expermental deposton correlatons, algebrac and frst order rate equatons, or stochastc modellng approaches, are stll valuable to readly obtan averaged partcle deposton data. Snce the dose dstrbuton due to the deposted radoactve partcles n lungs rather than ts average value s more crucal local dstrbutons of nhaled aerosols n the large central human arways are studed by usng the FLUENT CFD code. These smulatons hghlght the effects of partcle dameter, turbulent models, and flow rate on partcle deposton patterns n lungs

2 903. THEORY.1 Arway geometry In general, the lungs consst of a seres of bfurcatng tubes, where each bfurcaton leads to a new lung generaton numbered 1-3. The frst and stll wdely used mappng of the human lung was done by Webel [4] n 1963, known as the symmetrc planar Webel A model. Improvements were publshed such as Fnlay et al. [5] among others. Cytologcal studes of uranum mners show that the lung cancers have usually developed n the arway generatons 3-5, where the prmary deposton veloctes are the hghest. Thus, t s rather mportant to study the deposton of nhaled aerosol partcles n ths part of human arways n order to fnd relatonshp between the cellular dose and adverse health effects. In ths work, the GAMBIT software s used for formaton of 3D mesh structure of computatonal doman. In ths work, the symmetrc trple bfurcaton model s used to smulate the arways through generatons 3 to 6 as shown n Fgure 1. Fgure 1: Schematc of a symmetrc trple bfurcaton arway (generatons G3-G6). The unstructured grd s employed. The near wall meshes are refned to have a y+ value around 1. Ths y+ value allows utlzng enhanced wall treatment for standard k-e turbulence model. The number of 3D cells employed n the present smulatons s around Further ncrease n the number of computatonal cells dd not change calculated results sgnfcantly. The szes used n ths study regardng to each arway are the ones taken from mproved mappng of the human lung of Fnlay [5] as tabulated n Table 1. Table 1: Szes of broncha generatons G3 through G6 Generaton Fnlay et al. model length (cm) Fnlay et al. model dameter (cm) Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

3 Governng Equatons..1 Governng Equatons for Ar Flow One of the objectves of ths study s to nvestgate turbulent models effects on partcle deposton. The conservaton equatons for mass, momentum and energy and turbulent models used n ths study are outlned below Standard and Low Reynolds k- Models The contnuty, Reynolds averaged Naver-Stokes equaton and tme-averaged energy equaton are gven as follows [6]: u = 0, (1) x ρ u μ = + + j P u u j ' ' u ρuu j, () x x j x x j x T T ' ρcu p = k ρut ', (3) x x x where u and u are the velocty components n x and y drectons, respectvely, ρ s j the densty, P s the pressure, μ s dynamc vscosty, c p s the specfc heat, T s the temperature, k s the thermal conductvty. The Reynolds stress s related to the local velocty gradents by an eddy vscostyν t by usng the Boussnesq approxmaton. The turbulence scalar quanttes k and used to calculate ν t are obtaned from the followng modelled transport equatons: k μ t k u u j u ρu = μ+ + μt + ρ, (4) x σ x k x x j x x j μ t u u j u ρu = μ+ + f 1 C 1μt + ρ f C + E, x σ x x k xj x xj k (5) k μt = ρfc μ μ, (6) = +D, (7) ( ρ) ρk ρ ky ρ μ / y Re T =, Re y =, Re =, (8) μ μ μ where Cμ, C1, C, σ k and σ are the same emprcal turbulence model constants to those convenently n the hgh Reynolds number k model. In the current study followng values are used for the model constants: Cμ = 0.09, C1 = 1.44, C =.93, σ k =1.0 and σ = 1.3. The dumpng functons fμ, f1 and f, and D and E terms are used to make the low Reynolds number models vald n the near wall regon. The detaled physcal meanng of the dumpng functons and the D and E terms s gven n Ref. [7]. The dumpng functons for the varous low Reynolds number k models used n ths work are summarzed n Tables. 1/4 Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

4 903.4 Table : Summary of dumpng functons appearng n governng equatons Model f f μ 1 f Standard k 3/4 1 / 9exp( Re ) / 36 T AB tanh ( Re y)( 1+ 4 ReT ) ( Re y/1) AKN 3/4 { / Re exp T ( Re / 00) T } 1 exp( Re /14) 5/4 CHC 1 exp( Re ) y ( / ReT ) { 1 0.3exp ( Re T /6.5) } 1 ( Re /3.1) exp( Re ) T 1 exp( Re y ) Low Reynolds number turbulent models such as AB, AKN and CHC models tabulated n Table are not assocated wth the wall laws but make t to predct effectvely the dynamc, thermal, and turbulent behavour of ppe flows...1. Standard k-ω Model The standard k- ω model s an emprcal model based on modelled transport equatons for the turbulence knetc energy (k) and the specfc dsspaton rate (ω) whch can also be thought as the rato of to k. The transport equatons for the standard k- ω model are: ρ + ρ = Γ k ( k) ( ku) ( k ) + Gk -Yk + S k, (9) t z zj zj ω ( ρω) + ( ρωu = Γ ) ( ω ) + Gω -Yω + S ω. t z zj zj In these equatons, G k represents the generaton of turbulence knetc energy due to mean velocty gradents. G ω represents the generaton of ω. Γ k and Γ ω represent the effectve dffusvty of k and ω, respectvely. Yk and Yω represent the dsspaton of k and ω due to turbulence. and S are user-defned source terms. Sk.. Governng Equatons for Partcle Moton ω Moton of radoactve aerosol partcles suspended n the nhaled ar s analyzed by usng dscrete phase model of FLUENT. The partcle trajectory s calculated through ntegraton of the equaton of the balance of forces actng on the partcle. The equaton descrbng the partcle velocty, n the Lagrange formulaton, for the z-component of Cartesan coordnate system has the form Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

5 where du dt g ( ρ - ρ) = FD ( u- up) + + Fz, (10) ρ p x p u p and u are the partcle and ar veloctes, p ρ p and ρ are the partcle and ar denstes, F n Eq.(10) expresses the sum of the all respectvely, and g s the gravtatonal acceleraton. z external forces actng on the partcle suspended n the ar. For the purpose of ths analyzes Brownan moton and Saffman s lft force are consdered. Detals of components of Brownan force and Saffman s lft force could be found n Ref. [8]. Here, F D s the drag force calculated from the expresson: 18μ CD Re FD =, (11) ρ d 4 p where μ s the ar vscosty, p d p s the partcle dameter and the Reynolds number s defned as ρdp up -u Re =. (1) μ The drag coeffcent C D s calculated from the followng expresson: a a3 CD = a1 + + (13) Re Re where a 1, a, and a 3 are constants that apply to smooth sphercal partcles over several ranges of Re number gven by Mors and Alexander [9]. 3 RESULTS AND DISCUSSION In general, breathng patterns are pulsatle n nature. However, Zhang et al. [10] have proposed a matchng Reynolds number,.e. an nlet Reynolds number Rematch 0.5( Remean + Remax ) representng the nhalaton cycle. For the steady nhalaton phase a unform velocty profle calculated from matchng Reynolds number s specfed for the ar at the nlet of G3 bronch generaton. The ntal partcle veloctes are set equal to that of ar. The boundary condtons for governng equatons nclude symmetry wth respect to the plane of the bfurcaton, and no slp at the rgd the rgd mpermeable walls. At the outlet unform pressure condton s employed. Fgure depcts the computed flow patterns n bronchal generatons G3 through G6 at a constant restng nhalaton rate of Q=15 l/mn. Flow feld computatons are only presented for k ω model for llustratve purposes. The remanng models employed n ths work,.e. standard and low Reynolds k models, produce very smlar flow patterns. In Fgure 3, the computed flow patterns n bronchal generatons G3 through G6 at a constant moderate exercsng nhalaton rate of Q=60 l/mn are llustrated. Comparson of Fgures and 3 demonstrates strong dependency of flow felds on nhalaton rate. It could also be notced that downstream flow peakng becomes more pronounced as nhalaton rate ncreases. Hence, t could be presumed that deposton hot spots of the nhaled aerosol partcles wll be relatvely more concentrated around the mdway of the frst generaton bronch as bfurcaton goes on. Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

6 903.6 Fgure : Contours of Velocty Magntude (m/s) at Rest (Q = 15 l/mn) Fgure 3: Contours of Velocty Magntude (m/s) Durng Moderate Exercse (Q = 60 l/mn) For the partcle trajectory and deposton pattern smulatons through arway generatons G3-G6, aerosol partcles are njected at the nlet of G3. The dstrbuton of these randomly njected partcles follows the nlet velocty profle of the ar. The 3-D vews of the local partcle deposton patterns n terms number of partcles deposted for partcles wth aerodynamc dameters 1 and 10 μm are shown n Fgures 4 and 5, respectvely. In both cases, computatons are carred out wth k ω model for restng nhalaton condtons. Mcropartcle deposton durng nhalaton s manly due to mpacton, secondary flow convecton, and turbulent dsperson. As a result, mcron-sze partcles manly accumulate at stagnaton ponts for axal partcle moton and the regons just upstream of the straght bronch tube. The contrbuton of turbulent dsperson on deposton s stronger for small-sze partcles; say 1 μm, than for larger-sze partcles as seen from the fgures. In Fgures 6 and 7, smlar to restng case, local deposton patterns of deposted partcles wth aerodynamc dameters 1 and 10 μm are shown for moderate exercse condton. For large-sze 10 μm partcles at moderate exercse case, most of the deposton occurs n the frst generaton Bronch G3 as seen from Fgure 7. Ths could be attrbuted to the mpacton and nertal effects whch domnate over other forces actng on the aerosols. Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

7 903.7 Fgure 4: Deposton patterns of 1 μm partcles through bronch generatons G3-G6 at restng nhalaton rate (Q=15 l/mn) computed usng k ω model Fgure 5: Deposton patterns of 10 μm partcles through bronch generatons G3-G6 at restng nhalaton rate (Q=15 l/mn) computed usng k ω model Fgure 6: Deposton patterns of 1 μm partcles through bronch generatons G3-G6 at moderate exercse nhalaton rate (Q=60 l/mn) computed usng k ω model Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

8 903.8 Fgure 7: Deposton patterns of 10 μm partcles through bronch generatons G3-G6 at moderate exercse nhalaton rate (Q=15 l/mn) computed usng k ω model The regonal deposton of partcles n human arways can be quantfed n terms of deposton effcency (DE) n a specfc regon (e.g., oral arway, frst, second, and thrd bfurcaton etc.). It s defned as the rato of the number of deposted partcles n a specfc regon to the number of the partcles enterng ths regon. Of nterest are deposton effcences as well as deposton patterns from nano-sze partcles range (10 nm) to mcrosze partcles range (10 μm). Fgures 8, 9, 10, 11, and 1 depct partcle deposton effcences for bronch generatons G3 through G6 at restng and moderate exercsng nhalaton condtons for the specfed range of partcle aerodynamc dameters. Fgure 8 llustrates DE values computed usng k ω model. In Fgures 9,10,11, and 1, DE values computed usng Standard k Model as well as some three of Low Reynolds Number k Models (AB, AKN, CHC), respectvely, are presented. When the DE values of dfferent models are compared n Fgures 8-1, t becomes apparent that k ω model and low Reynolds number k models apply equally well n partcle deposton computatons. Results of low Reynolds number k models as well as k ω model are found n perfect agreement wth the results of Ref. [11]. Standard k model DE values consderably dffer from the results of other models and t seems not a sutable model for partcle deposton computatons n tracheal bfurcatons. Fgure 8: Deposton effcency (DE) vs. partcle dameter n k ω turbulence model. Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

9 903.9 Fgure 9: Deposton effcency (DE) vs. partcle dameter n standard k turbulence model. Fgure 10: Deposton effcency (DE) vs. partcle dameter n low Reynolds number AB k turbulence model. Fgure 11: Deposton effcency (DE) vs. partcle dameter n low Reynolds number AKN k turbulence model. Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

10 Fgure 1: Deposton effcency (DE) vs. partcle dameter n low Reynolds number CHC k turbulence model. CONCLUSIONS It s observed that deposton patterns n tracheal bfurcatons are not very senstve to the partcle sze for small mcron sze partcles at low nhalaton rates. Major deposton mechansm durng nhalaton of small sze mcron and nano-partcles s demonstrated to be dffuson at the tracheal walls whch allows penetraton of aerosols to the further trachea. At hgh nhalaton rates, mpacton s observed to become more pronounced especally for large aerodynamc dameter aerosol partcles; as a result, most of the partcles are deposted n the man arway generaton. Hot spots of deposton mostly occur n the vcnty of carnal rdge and at the nner sdes of the daughter arways downstream of the carna. It s shown that k ω and low Reynolds numbe r k models of FLUENT such as AB, AKN and CHC produce results whch are n perfect agreement among themselves and wth the lterature for partcle deposton computatons. It s also shown that standard k model s not sutable for analysng aerosols deposton n human respratory system. Consderng the fact that the dose dstrbuton due to the deposted partcles n lungs rather than ts average value s more crucal, t s demonstrated n ths work CFPD smulatons are very convenent tools to estmate local depostons of radoactve aerosols. Based on the deposton calculatons presented n the current study, local dose dstrbuton n lungs due to radoactve partcles ntake could be determned as a further step whch wll be the subject of our next study. REFERENCES [1] C. Klenstreurer, Boflud Dynamcs, Prncples and Applcatons, CRC Taylor&Francs, Boca Raton, 006, pp. 398, [] J. H. Goo, C.S. Km, Theoretcal analyss of deposton of nhaled partcles n human lungs consderng stochastc varatons of arway morphology, Journal of Aerosol Scence, 34, 003, pp Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008

11 [3] W. Hofmann, B. Asgharn, R. Wnkler-Hel, Modelng ntersubject varablty of partcle deposton n human lungs, J ournal of Aerosols Scence, 33, 00, pp [4] E.R.Webel, Morphometry of the Human Lung, Academc Press, New York, [5] W. H. Fnlay, The Mechancs of Inhaled Pharmaceutcal Aerosols: An Introducton, Academc Press, London, 001. [6] S. J. Wang, A. S. Mujumbar, A comparatve study of fve low Reynolds number k models for mpngent heat transfer, Appled Thermal Engneerng, 5, 005, pp [7] V. C. Patel, W. Rod, G. Scheuerer, Turbulence models for near-wall and low Reynolds number flows: a revew, the Amercan Insttute of Aeronautcs and Astronautcs, 3, 1985, pp [8] A. L, G. Ahmad, Dsperson and deposton of sphercal partcles from pont sources n a turbulent channel flow, Aerosol Scence and Technology, 16, 199, pp [9] S. A. Mors, A. J. Alexander, An Investgaton of Partcle Trajectores n Two-Phase Flow Systems, Journal of Flud Mechancs, 55(), 199, pp [10] Z. Zhang, C. Klenstreuer, Transent arflow structures and partcle transport n a sequentally branchng lung arway model, Physcs of Fluds, 14, 00, pp [11] I. Balásházy, Á. Farkas, I. Szőke, Smulaton of arflow, aerosol deposton and clearance n central human arways, Internatonal Austran-Israel Technon Symposa, Partculate Matter and Health, Venna, February 4-6, 003. Proceedngs of the Internatonal Conference Nuclear Energy for New Europe, Portorož, Slovena, Sept. 8-11, 008