Modelling of two-phase, transient airflow and particles

Journal of Turbulence

ISSN: (Print) 1468-5248 (Online) Journal homepage: http://www.tandfonline.com/loi/tjot20

Modelling of two-phase, transient airflow and particles distribution in the indoor environment by Large Eddy Simulation D. P. Karadimou & N. C. Markatos To cite this article: D. P. Karadimou & N. C. Markatos (2016) Modelling of two-phase, transient airflow and particles distribution in the indoor environment by Large Eddy Simulation, Journal of Turbulence, 17:2, 216-236, DOI: 10.1080/14685248.2015.1085124 To link to this article: http://dx.doi.org/10.1080/14685248.2015.1085124

Published online: 02 Dec 2016.

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Date: 07 December 2015, At: 13:45

JOURNAL OF TURBULENCE,  VOL. , NO. , – http://dx.doi.org/./..

Modelling of two-phase, transient airflow and particles distribution in the indoor environment by Large Eddy Simulation D. P. Karadimou and N. C. Markatos

Downloaded by [Despoina Karadimou] at 13:45 07 December 2015

Computational Fluid Dynamics Unit, School of Chemical Engineering, National Technical University of Athens, Athens, Greece

ABSTRACT

ARTICLE HISTORY

Prediction of particles distribution in the smaller-scale atmospheric environment, such as the indoor atmosphere, is of major importance for the comfort and the well-being of its occupants. The objective of this study is to investigate the airflow and particles transport, as well as the particles concentration evolution indoors, using Computational Fluid Dynamics (CFD) techniques. A three-dimensional, Euler–Euler two-phase flow model for the investigation of the indoor aerosol is developed, within a CFD general-purpose computer program (PHOENICS), and is validated against experimental measurements from the literature, for an ordinary case of indoor dilute aerosol. Turbulent flow is simulated by Large Eddy Simulation (LES) and the results are compared with those obtained applying the Reynolds-averaged Navier– Stokes (RANS) equations together with the ReNormalisation Group (RNG) k–ε model. Two-way coupling between the two phases is modelled by means of appropriate interphase interactions. This study focused on particles of one size group (mean aerodynamic diameter of 10 µm) but the numerical method described can equally well be applied for a broader size range. It is concluded that for the very dilute aerosols considered here, simpler models (such as single-phase and drift flux) do as well in predicting the important parameters of the flow, as the more complex ones.

Received  January  Accepted  August  KEYWORDS

Computational fluid dynamics; air-particles dispersed flow; Euler–Euler two-phase flow model; Large Eddy Simulation; particle concentration; indoor atmosphere

Nomenclature P ri ϕi ρi ui , ν i , wi Vi φ ,i Sϕ ,i k

CONTACT N. C. Markatos ©  Taylor & Francis

Atmospheric pressure Volume fraction of each phase i Dependent variable of each phase i Density of each phase i Three components of velocity for each phase i Velocity magnitude of each phase i Within-phase diffusion coefficient Within-phase volumetric source Turbulence kinetic energy

[email protected], [email protected]

Pa m /m Kg/m m/sec m/sec Kg/m sec m /sec


JOURNAL OF TURBULENCE

ε λij νt h α s

xk ui Ff,ip CD Rep d µ Vslip Ti Subscripts i g p in avg h Abbreviations ACGIH AED CFD D EPA IPSA LES N-S PHOENICS PM RANS RNG SARS SGS VOCs

Dissipation rate of turbulence Leonard stresses Turbulence viscosity Turbulence length scale Smagorinsky constant Stress strain rate Effective filter width Spatially-filtered velocity Frictional force per unit volume at the gas–particle interphase Drag coefficient Particle Reynolds number Diameter Dynamic viscosity Relative velocity between the two phases Turbulence length scale Turbulence intensity

217

m /sec m m m/sec N/m µm kg/msec m/sec m %

Index for phases Gaseous phase (air) Particulate phase Inlet Mean value Hydraulic American Conference of Governmental Industrial Hygienists Aerodynamic diameter Computational fluid dynamics Three dimensional Environmental Protection Agency Interphase slip algorithm Large Eddy Simulation Navier–Stokes Parabolic hyperbolic or elliptic numerical integration code series Particulate matter Reynolds-averaged Navier–Stokes equations ReNormalisation Group Severe acute respiratory syndrome Sub-grid scale Volatile organic compounds

1. Introduction 1.1 Aerosols in the indoor environment Aerosols are formed by small particles suspended in air, either emitted as primary aerosols or formed as secondary products of air chemical reactions (secondary aerosols). The total mass of aerosols per unit volume is designated as particulate matter, ‘PM’.[1] PM-10 and PM-2.5 is the mass per m3 of air sampled that passes through a pre-collector with a 50% efficiency at a 10 and 2.5 µm aerodynamic diameter (AED), respectively. Thus, PM-10 includes particles up to about 10 µm AED and PM-2.5 includes particles up to about 2.5 µm AED.[2] Indoor particulate matter is one of the most important indoor air pollutants involved in a number of adverse health effects. Hazardous influence of particles is related to their penetration and deposition into the human respiratory system. According to the ACGIH,[3] particulate matter is separated into three categories, including inhalable, thoracic and respirable particles. The inhalable fraction of particles can be described as all of the particulate matter in the air that can be taken in by the human respiratory system. The thoracic fraction of particles represents particles that can penetrate to the lower thoracic regions of the


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D. P. KARADIMOU AND N. C. MARKATOS

human respiratory system and refers to particles with AED less or equal to 10 µm. The respirable particles, with AED less or equal to 2.5 µm are those particles which can penetrate to the terminal bronchioles. The inhalable particles can be deposited on the nasal passage causing irritation to airways and skin as well as allergy. Especially, the thoracic particles may have serious adverse health effects, and according to epidemiological studies, there is a relationship between mortality rates and concentrations of respirable particles.[3–5] Furthermore, some infectious diseases, such as Ebola, flu, tuberculosis, SARS and the avian influenza (commonly bird flu) may be transmitted by airborne particles that contain or carry the viruses, resulting in the spread of diseases.[6,7] Indoor particle concentration depends on penetration of outdoor particles into the indoor environment and on the intensity of indoor aerosol sources. The indoor sources have been classified into six types of aerosols: (1) bioaerosols (plant and animal), (2) mineral, (3) combustion, (4) home/personal care and (5) radioactive aerosols.[8] Particles in the indoor environment may be deposited on interior surfaces that result in dirty floors and windows in the home and office, failure of precision machinery, soiled and discoloured art work in museums.[8] As far as the architectural aspect is concerned, changes in the building design devised to improve the energy efficiency have meant that modern homes and offices are frequently more airtight than older structures. Furthermore, advances in the construction technology have caused a much greater use of synthetic building materials. Whilst these improvements have led to more comfortable buildings with lower running costs, they also provide indoor environments in which contaminants are readily produced and may build up to much higher concentrations than are found outside. Additionally, if the structure of a building begins to deteriorate, exposure to asbestos may be an important risk factor for the chronic, respiratory disease mesothelioma. Of particular importance might be substances known as volatile organic compounds (VOCs),[9] which arise from sources, including paints, varnishes, solvents, and preservatives. The health effects of inhaled biological particles can be significant, as their role in inducing illness through immune mechanisms, infectious processes and direct toxicity is considered. Outdoor sources can be the main contributors to indoor concentrations of some contaminants. Of particular significance is radon, the radioactive gas that arises from outside, yet only presents a serious health risk when found inside buildings. Radon decays to form radon progeny through nuclear degradation that is electrically charged and can be attached to airborne particles.[10] According to EPA, nowadays people in developed countries typically spend 90% of their time indoors, a fact that has motivated increasing concern within the scientific community over the effects of indoor aerosols on health. Mathematical models of indoor exposure can play an important role in better understanding the mechanism of particle dispersion, since full-scale experiments with adequate instrumentation are often difficult to perform due to size, cost and adverse conditions. Various indoor exposure modelling techniques are available, ranging from simple statistical regression and mass-balance approaches, to more complex multizone and CFD tools.[11,12] Generally, particle sizes are categorized into three modes [13]: ultrafine (smaller than 0.1 µm), accumulation (0.1–2 µm) and coarse (larger than 2 µm). The size group of the particles studied here (AED 10 µm) belongs to the coarse mode. However, the general conclusions derived at by the present work are also valid for a broader particle size range.


219


1.2 Historical background The numerical simulation of particles transport by a fluid carrier requires the modelling of the continuous phase (fluid), of the discrete phase (particles) and of their interactions. The continuous phase (liquid or air) is modelled using an Eulerian formulation. The discrete phase (droplets, bubbles or particles) may be modelled using either an Eulerian or a Lagrangian approach. In the Eulerian approach, particles are treated as a continuum and in the Lagrangian approach, each particle trajectory is simulated. The Eulerian–Eulerian method can be employed either using a one-phase flow formulation or a two-phase flow formulation. In the one-phase flow formulation, the mixture is considered as a whole and it is represented by a single continuity equation, one momentum equation in each coordinate direction and one convection–diffusion equation, to take into account the effect of concentration gradients. The particle velocity is not calculated by the particles momentum differential equation but it is determined by an algebraic equation for the particle-fluid slip velocity, implemented into the source term of the equation.[14,15] Many studies have been conducted until recently to simulate the indoor aerosol using either the Eulerian–Lagrangian approach [15–40] or the one-phase flow Eulerian approach.[15,19,27,29,37,39–53] Markatos et al. [41] studied the effect of turbulence on the diffusion rate in a buoyancy dominated problem of smoke flow in an enclosure by using a concentration equation. Most of the aforementioned one-phase flow Eulerian approach studies for the airflow and particle transport in the indoor environment, also called drift flux models, use the convection–diffusion equation assuming the gravitational settling, the Brownian and turbulence diffusion effect and the deposition model of Lai and Nazaroff [54], for taking into account the concentration gradient in the boundary layer. According to this concept, the particles are treated as static entities and focus is placed on the details of transport, rather than other aspects of particle dynamic behaviour.[13] However, much more detailed treatment of two-phase motions through an Eulerian–Eulerian model is also possible.[12] Several authors including Vernier and Delhaye [55]; Kuo et al. [56]; Ishii [57]; Ishii and Mishima [12]; Drew and Lahey [58]; Spalding [59]; Markatos et al. [60]; Markatos [61]; Crowe et al. [62] have defined an essentially Eulerian–Eulerian theoretical method, called the ‘two-phase flow-dynamic model of interdispersed continua’. The focus of this study is to simulate the particle dispersed indoor airflow using a latter type two-phase flow Eulerian–Eulerian model and compare the results with those of simpler models. The general method employed in this study follows the so-called ‘control volume’ approach,[59] which is developed by formulating the governing equations on the basis that mass and momentum fluxes are balanced over control volumes occupied by spacesharing interspersed continua. According to that concept,[61] distinct phases are present within the same space (although never at precisely the same time), their shares of space being measured by their ‘volume fractions’. According to Elgobashi,[63] a criterion to determine the type of interaction in terms of the volume fraction of particles (r p ) is as follows: r p ≺ 10−6 , for one-way coupling 10−6 ≤ r p ≤ 10−3 , for two-way coupling r p 10−3 , for four-way coupling. Although the volume fraction of particles indoors is, in general, very low,[49] the twoway coupling interaction type is applied to investigate the dispersion of dilute mixtures of

220


particles in the indoor environment, so that more details of the particle dynamic behaviour are taken into account. The two-phase flow model for dilute mixtures of particles has also been adopted by other authors [64] in the case of aerosol laminar flow in a bend of circular cross section, as it is more general and more accurate than the alternatives.

2. Mathematical modelling


2.1 The governing differential equations and the dispersed-solid drag model Mathematical modelling consists of the Navier–Stokes (N-S) equations and the continuity equation for a three-dimensional (3D) turbulent fluid flow. The equations are derived by considering the balance of fluxes over a control volume small enough to give the desired spatial distributions in the complete system, yet large enough to contain many solid particles, so that the averaged particle velocity and volume fraction are meaningful.[59] The control volume can be regarded as containing a volume fraction of each phase (ri ), so that if there are two phases together rg + rp = 1. Each phase is treated as a continuum in the control volume under consideration. The phases share the control volume and they may, as they move within it, interpenetrate.[61] Particles can be treated as a continuum when the particle size is significantly smaller than the Kolmogorov microscale of the airflow field and each control volume contains a sufficient number of particles, so that particles statistically averaged properties are valid. The Kolmogorov microscale is at the magnitude of 1 mm for a normal ventilated room,[65] which is several orders of magnitude larger than the indoor particle sizes. The assumptions made for the present flow model are the following: (1) The two phases are assumed interdispersed and coupled by the interphase friction as the appropriate interaction term. (2) Each phase is a continuum, so that the derivatives are uniquely defined. (3) Incompressible flow of a Newtonian carrier fluid (air). (4) Constant air and solid properties at 300 0 K and free of phase change. (5) No chemical reaction takes place. (6) Spherical monodisperse particles of one size group (mean AED 10 µm). (7) Inter-particle collisions are neglected. (8) The motion of each isolated particle is not influenced by the wake of the others. (9) Turbulence is accounted for only in the gaseous phase as it affects both phases, while the particulate-phase turbulence does not. The above assumptions are certainly reasonable for the dilute mixtures considered here. .. RANS modelling – governing equations The general form of all the governing differential conservation equations applied by the RANS mathematical model is presented below [59]: ∂ → (ri ρi ϕi ) + div(ri ρι ui ϕι − ri ϕ,ι gradϕι ) = Sϕ,i , ∂t where φ i is the dependent variable of each phase i,

(1)


221


ri is the volume fraction of each phase, ρ i is the density of each phase, ui is the velocity vector of each phase, φ ,i is the within-phase diffusion coefficient and Sφ ,i is the within-phase volumetric source. The within-phase diffusion term represents the molecular and turbulent mixing terms present for each phase. The dependent variables solved for are: (1) pressure, assumed here to be the same for both phases, P, (2) volume fractions of each phase, ri , (3) three components of velocity for each phase ui ,v i ,wi and (4) turbulence kinetic energy and dissipation rate of turbulence for the gaseous phase, k and ε. The phase volume fraction equation [61] is obtained from the continuity equation: → ∂ (ri ρi ) + div(ri ρi u i ) = Sϕ,i , ∂t

(2)

where ri = phase volume fraction, m3 /m3 ρi = phase density, kg/m3 i = phase velocity vector, m/sec u Sϕ,i = net rate of mass entering phase i from phase j, kg/(m3 sec), if there is a phase change. Particles are assumed to be transported and dispersed due to turbulence of the carrier fluid (air), while their movements do not affect the airflow turbulence (one-way coupling). Turbulent flow of the carrier fluid (air) is simulated using a RANS mathematical model, the RNG k–ε model.[66] The RNG k–ε model appears more suitable for indoor airflow simulation, leading to better agreement between simulated results and the measured data, compared to the standard k–ε and other turbulence models [67,68, unpublished work by the present authors]. The LES approach is, however, conceptually at least more suitable; therefore, LES modelling was also performed for comparison purposes. .. LES – governing equations In LES, the large turbulence scales of the air phase, containing most of the energy, are resolved explicitly, while only the sub-grid scales (SGS) containing a small fraction of the energy are modelled [69,70 and references therein]. A spatial filtering is applied to every variable of the flow field, decomposing it into a resolved (or filtered) component and a SGS component. The filtered governing equations, adapted in this study for two-phase flows, are presented below[69] ∂ri u¯ ∂ri + =0 ∂t ∂x j ∂ u¯ j ∂ u¯i ∂ ∂ 1 ∂p ∂ri u¯i , + ri u¯i u¯ j + λi j = −ri + ri (v + vt ) + ∂t ∂x j P ∂xi ∂x j ∂x j ∂xi

(3) (4)

222



where ( xk )2 ∂ 2 u¯i u¯ j λi j = 6 ∂xk ∂xk

(5)

vt = a1 h2 s−1/2

(6)

h = 81/3 ( x1 x2 x3 )1/3 ∂ u¯ j ∂ u¯i ∂ u¯i + , s¯ = ∂x j ∂xi ∂x j

(7) (8)

where λi j are the Leonard stresses, νt is the turbulence viscosity, h is the turbulence length scale, a1 is the Smagorinsky constant, s¯ is the stress strain rate, xk is the effective filter width, u¯i is the spatially filtered velocity. The LES model in the Eulerian–Eulerian approach is active on both air- and particulate phases. .. Solid-drag mathematical model The frictional force Ff ,ip per unit volume at the gas–particle interphase, due to differing phase velocities is [12] Ff ,ip = 0.5CD A pr ρg Vg − Vp Vg − Vp ≡ C f ,ip Vg−Vp ,

(9)

where CD is the drag coefficient, A pr is the total projected area of particles per unit volume, ρg is the density of the gaseous phase, Vg is the gaseous phase velocity, Vp is the particulate phase velocity and C f ,ip is the interphase friction coefficient. The empirical correlation used for CD is the Stoke’s drag law [71] CD =

24 , Re p

(10)

where Re p is the particle Reynolds number defined as [72] Re p =

d pρ p Vslip , μg

(11)

where d p is the particles diameter, ρ p is the particles density, μg is the dynamic viscosity of the gaseous phase and Vslip is the relative velocity between the two phases. .. Boundary conditions For the carrier fluid phase – the mass flow rate multiplied by the volume fraction is defined at the inlet. A Dirichlet condition is also applied, by setting a uniform velocity (0.225 m/sec) in the flow direction. For the particulate phase – the mass flow rate multiplied by the volume fraction is defined at the supply inlet. A uniform velocity (0.225 m/sec) for the particulate phase in the flow direction is also applied.


223

The turbulence kinetic energy of the air phase that is applied at the inlet, when the RNG k-ε model is used, is defined as [73] kin =

3 (Uavg Ti )2 , 2

where Uavg is the mean air inlet velocity and Ti the turbulence intensity, considered 6%.[74,75] The dissipation rate is given by


εin = Cμ 3/4

k3/2 ,

where is the turbulence length scale assumed to be = 0.07 dh (dh hydraulic diameter of the duct) and Cμ = 0.0845 is an empirical constant of the turbulence model. At the outlet, a uniform external pressure for both phases is specified. Particles in a ventilated room are most likely to attach to the surface since they usually cannot accumulate enough rebound energy to overcome adhesion;[76] thus, at the walls, the no-slip and no-penetration condition is applied for both phases. According to Louge et al.,[77] in very dilute suspensions, the law of the wall is not greatly affected by the presence of particles, thus the ‘logarithmic wall-functions’ are applied to the near wall grid points [78] for the gaseous phase when the RANS mathematical model is used. The walls are assumed adiabatic. 2.2 Computational fluid dynamics simulation The equations are discretised by the finite volume method and solved by the IPSA algorithm,[59,79,80] all embodied in the CFD code PHOENICS.[81] A fully implicit method is employed for the numerical solution. The convection terms of the RANS model conservation equations are discretized (1) by the upwind discretization scheme [82] and (2) by the van Leer numerical scheme.[83] The convection terms of the LES model equations are discretised by the van Leer numerical scheme.[83] The diffusion terms in both models are discretised by the central-differencing scheme. The first-order fully implicit scheme is used for time discretisation.

3. Validation of the CFD turbulence mathematical models – the physical problem considered The numerical model developed in this study is validated against experimental measurements.[43] Chen et al. measured the airflow field and particle concentration in a scale model room, presented in Figure 1, ventilated with an axial fan and supplied with a solid particle disperser ensuring a stable particle flow rate. Since this research provided all necessary experimental details, it is used for model validation. The aforementioned model room with dimensions width (X) × height (Y) × length (Z) = 0.4 m × 0.4 m × 0.8 m has two openings of the same size (0.04 m × 0.04 m), one being at the upper height of the upward side and the other at the lower height of the backward side of the room (Figure 1). Their centres are located at x = 0.2, y = 0.36 m, z = 0.0 m and x = 0.2 m, y = 0.04 m, z = 0.8 m, respectively. The openings communicate


224


Figure . Geometry of the physical problem.

with the outdoor environment through two ducts of the same size. The particles used in the experiment were silver-coated hollow glass beads with a nominal diameter range between 2 and 20 µm, a mean size of 10 µm and a material density of 1400 kg/m3 .

3.1 Grid- and time-step independency studies Grid and time-step independency is tested by repeating the numerical simulations, applying both mathematical models, for gradually increased grid-cell densities and various smaller time steps. For the LES grid-independency study, four grids were used (414.400, 676.800, 960.960, 1.834.560 cells). With each grid, the calculations were repeated for at least four different time steps and for each time step different numbers of iterations, gradually increased, were tested, in order to ensure solution convergence. For example, in the third grid (960.960 cells) the calculations were repeated for six different time steps (1, 0.5, 0.25, 0.1, 0.05, 0.02 sec) and in each step various numbers of iterations were used (within the range 20–400). In Figure 2, the vertical velocity distribution as predicted by the third grid for various time steps is presented. Finally, the numerical results for each variable as obtained by each grid applying the relevant optimum time step were compared in various regions of the domain. In Figures 3 and 4, the vertical velocity – and the volume fraction – distributions are presented in two different regions of the domain. According to the overall independency study, the analysis of the numerical results for the LES modelling is based on the third grid (960.960 cells) with time step 0.02 sec applying 40 iterations per time step. A similar grid- and time step- independency procedure was carried out for the RANS modelling. Four grids were used (40.000, 80.000, 160.000, 320.000 cells) and with each grid the calculations were repeated for four different time steps (1, 0.5, 0.25, 0.1 sec). In each time step, different numbers of iterations were tested in the range 20–400 with the aim to ensure solution convergence. According to the overall numerical results, an optimum solution was obtained, and thus, the analysis is based on the second grid (160.000 cells) with time step 1 sec and 100 iterations per time step. Apart from the regions near the walls


225

0.40 0.35 0.30 0.25 height (m)

0.20 0.15 0.10 0.05


-0.06

0.00 -0.02 0.00 velocity (m/sec)

-0.04

1

0.5

0.25

0.1

0.05

0.02

0.04

0.06

0.02

Figure . Vertical velocity-distribution predicted by the LES model based on the third grid (. cells) applying six different time steps (, ., ., ., ., . sec). 0.40 0.35 0.30 0.25 height (m)

0.20 0.15 0.10 0.05

-4.00E-02

-2.00E-02 414.400

0.00 0.00E+00 velocity (m/sec)

676.800

960.960

2.00E-02

4.00E-02

1.834.560

Figure . Vertical velocity-distribution predicted by the LES model applying four different grids (., ., ., .. cells) and the relevant optimum time step for each grid.

where grid lines are set, such that y+ is between 11.5 and 35, the grid in all other areas is uniformly distributed.

4. Results and discussion 4.1 Air-flow velocity distribution The developed model has been used for the study of indoor airflow and particle movement as well as particle concentration in the scale model-room. First, a steady-state numerical simulation is performed applying the RANS model to compare the numerical solution of

226


0.40 0.35 0.30 0.25 height (m)

0.20 0.15 0.10 0.05 0.00 0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04 5.00E-04 6.00E-04


volume fraction (m3/m3) 414.400

676.800

960.960

1.834.560

Figure . Volume fraction predicted by the LES model applying four different grids (., ., ., .. cells) and the relevant optimum time step for each grid.

velocity distribution with the available experimental data. The predicted steady-state airflow field in terms of velocity distribution is depicted in Figure 5, at the longitudinal centre plane of the domain. Due to the high value of interphase friction, the predicted steady-state particulate-phase flow field, in terms of velocity distribution, exhibits more or less the same flow pattern, thus it is not presented here.

Figure . Velocity distribution at the longitudinal plane of the domain.



227

Air recirculation is clearly observed in the domain, as expected. In Figure 5, an eddy is produced at the left corner near the floor of the domain as soon as air moves upwards, and two eddies are also produced at the left and the right corner of the ceiling in the air-flow pattern predicted by the RANS modelling. According to Lai and Chen,[28] the study of the same physical problem results in a velocity flow pattern with two eddies at the two corners of the ceiling and an eddy near the left corner of the floor, in agreement with the present results. The comparison of the numerical and experimental results of the air-phase vertical velocity component in the flow direction applying the RANS model is presented in Figures 6–8. The LES model was not applied for steady-state calculations. Figures 6–8 present the results obtained by the two-phase flow model applying the RNG k–ε turbulence model that are in acceptable agreement with the experimental measurements. .. LES airflow-field In this study, the LES model was applied in unsteady conditions. As far as the air-flow field is concerned, the LES model, is expected, to predict more details of the turbulent motion 0.4

0.3

height 0.2 (m)

0.1

0

-0.1

0 0.1 0.2 velocity (m/sec) experimental solution numerical solution Chen et al

Figure . Vertical w -component of velocity distribution at distance . m from the supply inlet applying the RANS model and the upwind numerical scheme.

228


0.4

0.3


height 0.2 (m)

0.1

0

-0.1

0

0.1

0.2

velocity (m/sec) experimental solution

numerical solution

Chen et al

Figure . Vertical w -component of velocity distribution at distance . m from the supply inlet applying the RANS model and the upwind numerical scheme.

as it solves the large eddies explicitly. In Figure 9, instantaneous velocity variation, in the period 20–130 sec, is presented. Instantaneous velocity distribution varies with time and is unstable during all the time of calculations.

4.2 Particle concentration evolution The calculation of indoor air-particle concentration is done in this work by solving for the volume fraction distribution of the PM, as opposed to just solving only a concentration equation. Thus, the particle concentration evolution of indoor aerosol can be obtained by the temporal development of the 3D two-phase flow model. A transient numerical simulation is performed applying both turbulence mathematical models (RANS, LES) by means of the CFD code PHOENICS. The comparison of predicted numerical and experimental results of the particle concentration at three different locations for both RANS and LES simulations is presented in Figures 10–12. These figures present also the results of Chen et al. [43] obtained by means of a one-phase model after a sufficiently long time (1800 sec). Particle concentration values are normalized by the inlet concentration.


229

0.4

0.3


0.2 height (m)

0.1

0

-0.1

0

0.1

0.2

velocity (m/sec) experimental solution

numerical solution

Chen et al

Figure . Vertical w -component of velocity distribution at distance . m from the supply inlet applying the RANS model and the upwind numerical scheme.

2.50E-01 2.00E-01 1.50E-01 w1 (m/sec) 1.00E-01 5.00E-02 0.00E+00

20

40

60

80

100

120

t (sec) LES

Figure . Instantaneous velocity distribution predicted by LES in time period (–sec).

230


0.4

0.3

height (m)


0.2

0.1

0 0

0.5

1

1.5

normalized concentration (C/Co)

Chen et al RANS

experiment LES

Figure . Vertical particle-concentration distribution at distance . m from the inlet along the centreline applying: (a) the RANS model, (b) the LES model and the van Leer numerical scheme. 0.4

0.3

height (m) 0.2

0.1

0 0

0.5

1


Chen et al

experiment

RANS

LES

Figure . Vertical particle-concentration distribution at distance . m from the inlet along the centreline applying: (a) the RANS model, (b) the LES model and the van Leer numerical scheme.


231

0.4

0.3

height 0.2 (m)


0.1

0 0

0.5

1


Chen et al

experiment

RANS

LES

Figure . Vertical particle-concentration distribution at distance . m from the inlet along the centreline applying: (a) the RANS model, (b) the LES model and the van Leer numerical scheme.

Comparing the performance of the LES and RANS model, a highly more accurate numerical solution is obtained by the former especially in the region near the domain outlet, where an intensive flow recirculation takes place. Particularly, in Figure 12, the maximum relative error of the RANS modelling against the experimental data is 60% at the height 0.38 m, while the maximum relative error of the LES modelling against the experimental data is 15% at the same height. Although the LES two-phase model presents a better performance it is more expensive than the RANS model. Comparing the computational cost of the two mathematical models on the same hardware (linux operating system, 1CPU, 2.4 GHz, 8 MB total memory available), the LES model calculations took, as expected, longer (they lasted almost 168 hours instead of 2–3 hours computing time of the RANS model). It is confirmed that the two-phase flow model of indoor aerosol, though more expensive, leads also to a satisfactory prediction as the one-phase model. The Eulerian–Eulerian approach allows the simultaneous calculation of air- and particle-flow field taking into account the interfacial interactions between the two phases rather than solving a particulate transport equation based on a static velocity flow field. This leads to a more detailed prediction of the flow motions of both phases, that becomes obvious especially in cases of higher particulate volume fraction. In the case of dilute indoor aerosol, the one-phase model represents satisfactorily the flow-field characteristics and becomes a preferable option due to the low computational cost.

232


1.20E-10 1.00E-10 8.00E-11 τxy 6.00E-11 4.00E-11 2.00E-11 0.00E+00 -2

3

8

13

18


t (sec) LES

RANS

Figure . Averaged shear stress distribution τ xy obtained by LES and RANS in time period (– sec).

4.3 Averaged shear stresses The shear stresses τxy , τyz , τzx are calculated from the stresses by way of the following equation: ∗ du dv − , 0.5∗ (1 − Pr)∗ τxy = Y/ 1 − Pr2 dy dx

(12)

where Y is Young’s modulus and Pr is Poisson’s ratio. In Figure 13, the averaged shear stress distribution τ xy, as obtained by both mathematical models (LES, RANS) in the time period 0–18 sec, is presented.

5. Conclusions A 3D Eulerian–Eulerian model is developed of a ventilated scale model room, within the framework of the CFD general-purpose computer program PHOENICS, which account for the two-phase flow, interfacial phenomena and concentration evolution. The twofold objective of the study is to develop a two-phase flow model to investigate the aerosol transport in the indoor environment and to compare the performance of the LES and RANS modelling. The model is capable of evaluating the transport mechanism of a dilute air-particle flow by predicting the velocity profile of both phases and the interfacial momentum interaction term as well as the particle-concentration field, by calculating the volume fraction of both phases. In the Eulerian–Eulerian approach, both phases are treated as interpenetrating continua, which makes possible the simultaneous calculations of the velocity and particle concentration field taking into account the interfacial interactions. The physical advantage of the two-phase flow model is more obvious when the volume fraction of the particulate phase is higher.


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The numerical results of the velocity profile in the steady-state simulation agree well with the experimental data. In the transient simulation, the numerical results of particleconcentration evolution obtained by the LES mathematical two-phase model present remarkably higher accuracy in the recirculation region of the domain over RANS. The onephase model still remains an optimum option for calculating the particle concentration dispersion of dilute aerosol as it combines virtually equal accuracy and less computational cost than the present scientifically satisfying procedure, which is certain to be superior for denser cases.

Acknowledgements


The work was supported by the State Scholarship Foundation of Greece.

Disclosure statement No potential conflict of interest was reported by the authors.

Funding The work was supported by the State Scholarship Foundation of Greece.

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