Development and Performance of a Fluence Rate Distribution Model

Publication Date (Web): February 2, 2008 ... The logic used in developing the fluence rate distribution model and calculations for one of the three ra...
5 downloads 0 Views 2MB Size
Download PDF
Environ. Sci. Technol. 2008, 42, 1605–1614

Development and Performance of a Fluence Rate Distribution Model for a Cylindrical Excimer Lamp ZORANA NAUNOVIC, KELLY G. PENNELL, AND ERNEST R. BLATCHLEY III* School of Civil Engineering, Purdue University, West Lafayette, Indiana 47907-2051

Received April 24, 2007. Revised manuscript received September 13, 2007. Accepted October 3, 2007.

Ultraviolet disinfection systems employing excimer lamp technology represent a suitable choice in situations where lamp mercury content is restricted, or otherwise undesirable. The XeBr* excimer lamp emits nearly monochromatic radiation at 282 nm, and dose–response experiments with Bacillus subtilis spores have shown that it is germicidally effective. A numerical model was developed to describe the fluence rate (E′) distribution emanating from a cylindrical XeBr* excimer lamp, based on liquid water or air as the surrounding medium. The E′ distribution model is based on physical phenomena that are known to govern excimer lamps; the model also accounts for refraction, reflection, and absorbance effects of the quartz lamp envelope and the media surrounding the lamp. Measurements of the E′ distribution by local actinometry supported the validity of the numerical model. This model can be used as a component (submodel) of a more general model to simulate the behavior of photochemical reactors that employ excimer lamps as their source of electromagnetic radiation.

Introduction Design and performance analysis of photochemical reactors [e.g., ultraviolet (UV) disinfection systems] can begin with numerical simulations. These models generally incorporate numerical representations of fluid mechanics (e.g., by computational fluid dynamics), which in turn are integrated with a numerical simulation of the fluence rate (E′) distribution and a representation of the intrinsic kinetics of the relevant photochemical reaction(s) (1–4). The most frequently used fluence rate distribution models in the computer-aided design of disinfection reactors employing low-pressure mercury lamps as the UV source are variants of the Line Source Integration model and the Multiple Source Summation model (5, 6). Computational hardware and commercially available CFD packages have developed to the point where reliable, accurate simulations of fluid mechanics in photochemical reactors are possible. Similarly, experiment-based tools are commonly available to allow detailed, accurate representations of the intrinsic kinetics of photochemical reactions. However, mathematical simulations of E′ distributions generally are not as well-developed as the other two model components. Indeed, the ability of a photochemical reactor model to accurately predict performance is often limited by the accuracy of the E′ distribution model. * Corresponding author phone: (765) 494-0316; fax: (765) 4940395; e-mail: [email protected]. 10.1021/es070968w CCC: $40.75

Published on Web 02/02/2008

 2008 American Chemical Society

Excimer lamps provide an alternative to conventional mercury-based systems in situations where lamp mercury content is restricted or undesirable. Baseline experiments conducted with a XeBr* (the asterisk denotes an excited molecular complex, which has no stable ground state under normal conditions) excimer lamp demonstrated its germicidal UV output to be highly effective for inactivation of Bacillus subtilis spores and other microorganisms (7–9). Prior to this research, no code that accounted for the physical phenomena that are known to govern the E′ distribution around an excimer lamp was available. Accurate simulations of the E′ distribution within a reactor required the development of a new E′ distribution model. This new model, termed the surface power apportionment for cylindrical excimer lamps (SPACE) E′ distribution model, accounts for the geometry and emission characteristics of the XeBr* excimer lamp, which are fundamentally different from those of conventional mercury lamps that are commonly used for these purposes; it also provides a detailed accounting of the effects of absorption, dissipation, reflection, and refraction within the reactor system. The SPACE model fluence rate distribution simulations can be incorporated into computer-aided evaluations and designs of excimer-based air or water disinfection reactors. These reactors are being considered for the disinfection of water during long-term space missions and the disinfection of commercial aircraft cabin air (10).

Materials and Methods Microbial Inactivation Kinetics at 222 and 282 nm. The UV dose–response behavior of B. subtilis spores was measured at 222 and 282 nm using the output from KrCl* and XeBr* excimer lamps (Ushio America, Inc.). The lamps were housed in flatplate collimators. Dose–response experiments were also conducted with a low-pressure mercury lamp that emits germicidal UV radiation at 253.7 nm so that germicidal effectiveness of different radiation wavelengths could be compared, and also as a surrogate for the XeI* excimer lamp which emits essentially monochromatic radiation at 253 nm. The results of the experiments were presented by Pennell et al. (7). Although radiation at 222 nm elicits a faster inactivation response of the B. subtilis spores than radiation at 282 or 254 nm, common constituents in water (e.g., nitrate and humic substances) are known to be strong absorbers of UV radiation at wavelengths below approximately 240 nm. Employing radiation at 222 nm was shown to be impractical as the transmission of UV radiation through representative water samples at 222 nm is much poorer than at higher wavelengths of interest, i.e., at 282 nm. Therefore, subsequent experiments and numerical simulations were all based on the XeBr* excimer lamp. Numerical Methods: Modeling of the E′ Distribution. Excimer lamps using a silent discharge design typically consist of two coaxial cylindrical tubes; the inner tube is a highvoltage electrode, and the exterior tube is in immediate contact with a metal mesh that acts as the ground potential electrode (11). A schematic of this geometry is presented in Figure 1. The tubes are made of a dielectric material, usually quartz. A rare gas or a mixture of rare gases and halogens is contained between the inner and outer tubes at close to atmospheric pressure. The imposition of an electrical potential across the two dielectric barriers leads to the formation of an excited molecular complex, which has no stable ground state under normal conditions. This molecular complex is called an excimer, and it decomposes within nanoseconds, giving up its excitation (binding) energy in the form of UV photons at characteristic wavelengths (12). The VOL. 42, NO. 5, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

1605

FIGURE 1. Cylindrical dielectric barrier discharge excimer lamp configuration with an annular discharge gap (adapted from ref 11, with permission).

FIGURE 2. Photograph of microdischarges in xenon, emitting radiation peaking at 172 nm, having a half-width of 12–14 nm. The original size was 26 mm × 38 mm (11, with permission). wavelength of radiation is dependent upon the gas mixture present within the dielectric barrier. At atmospheric pressure and with the electrode configuration illustrated in Figure 1, electrical breakdown occurs in a large number of short-lived current filaments termed microdischarges, which are (roughly) evenly distributed across the entire discharge area and spread into a surface discharge at the dielectric, as depicted in Figure 2 (11, 13, 14). The SPACE E′ distribution model is based on the assumption that each microdischarge represents a point source emitting radially in all directions, and that radiation received at any receptor site around the excimer lamp can be calculated as a contribution from a large number of point sources. The cylindrical excimer lamp was represented as a collection of point sources, equally spaced 2 mm apart to represent the distribution of microdischarges (11). In excimer lamps that are driven by alternating current (AC) power sources, filaments are initiated in the reverse direction when the voltage changes sign (15). Therefore, surface discharges will occur in different regions (at both dielectric barriers) at different times. The SPACE model assumes that the instantaneous E′ distribution around an excimer lamp is the result of surface discharges at one dielectric surface. It was assumed that each surface discharge or point source was located at the internal surface of the external quartz envelope, or the outer dielectric layer. A conceptual schematic of this assumed configuration is also shown in Figure 3. The example geometrical distribution of radiation point sources reasonably approximates UV emissions from one-half an operating cycle of an excimer lamp. An alternative E′ distribution model that would simulate a full operating cycle of AC-driven excimer lamps would include a radiation point source distribution on both dielectric barriers. The E′ at any receptor site around the excimer lamp would be calculated as an average of the radiation contribution emanating from point sources on both dielectric barriers. The performance of such a model should 1606

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 5, 2008

be tested and may provide improved estimates of the E′ distribution. The SPACE model also accounts for radiation received at receptor sites through reflection off the internal electrode and reactor housing. The model also accounts for refraction, reflection, and absorbance effects of the quartz lamp envelope and the medium surrounding the lamp. The medium surrounding the excimer lamp is defined by its refractive index and absorbance. Therefore, by specifying these two parameters, the user can simulate the fluence rate distribution in air, water, or other media. In the model, radiation may be received at a receptor site from every hypothetical point source through as many as three different radiation pathways: a direct radiation pathway from the point source (PS) to the receptor site (RS), reflection off the internal high-voltage electrode, and reflection off the reactor housing. An illustration of the radiation pathways that contribute to the total radiation received at a receptor site from a point source is presented in Figure 4. The total fluence rate at the ith receptor site (RSi) can be expressed as the sum of contributions from all point sources that contribute to radiation received at RSi through any combination of the three possible radiation pathways. Details of the mathematical calculations for one radiation pathway are presented below; the logic used in developing the model to account for the other radiation pathways is in many ways similar to the logic used in modeling the direct pathway; as such, model development for the other radiation pathways is presented in the Supporting Information. Direct Radiation Pathway. A receptor site (RS) can receive radiation from a point source (PS) via two different types of direct radiation pathways, depending on the location of a PS in reference to the RS. The first direct radiation pathway, denoted as dir1, accounts for radiation from a PS that is transmitted through the exterior quartz (EQ) envelope and 2D , of π/2 radians at the refracted at a maximum angle, θsm,dir1,max exterior quartz-surrounding medium (EQ-SM) interface before reaching the RS. The location of these PSs is illustrated in the two-dimensional (2D) cross section of the excimer lamp in Figure 5. PSs from which direct radiation through the EQ quartz envelope is refracted at an angle greater than π/2 radians at the EQ-SM interface contribute radiation to the RS through a different direct pathway, denoted as dir2. The radiation first penetrates the excimer gas (EG) gap and is then refracted through the EQ envelope before it reaches the RS. Details about the dir2 pathway are included in the Supporting Information. Consider first the development of a 2D (i.e., planar) representation of the transmission of radiation from a point source to a receptor site via the dir1 pathway. It is assumed that the RS will receive radiation that is refracted at a maximum angle, θsm,dir1,max2D, of π/2 radians at the EQ-SM interface, from a PS that is indexed as maxdir1, PSmaxdir1. From this assumption and from Snell’s law, which governs the refractive and reflective behavior of radiation being transmitted through media interfaces, the maximum incident angle of radiation from PSmaxdir1 at the EQ-SM interface can be calculated: 2D 2D θeq,dir1,max ) arcsin[(nsm ⁄ nq) sin θ sm,dir1,max ] ) arcsin(nsm ⁄ nq) (1)

where nq and nsm are refractive indexes of quartz and surrounding medium (SM), respectively, θ2D eq,dir1,max is the maximum 2D is the incident angle at the EQ-SM interface, and θsm,dir1,max maximum refracted angle at the EQ-SM interface. The maximum path length of radiation transmitted 2D can be calculated from through the EQ dielectric, deq,dir1,max the law of cosines:

[

2D 2D ) 0.5 2RL cos θeq,dir1,max deq,dir1,max 2D )2 - 4(RL2 - (RL - tq)2)] √(2RL cos θeq,dir1,max

(2)

FIGURE 3. Conceptual schematic of the microdischarges represented as point sources within the SPACE fluence rate distribution model.

FIGURE 4. Illustration of three different radiation pathways from a point source to a receptor site (two-dimensional representation). where RL is the exterior lamp radius and tq is the thickness of the quartz envelope. The maximum angle among PSmaxdir1, lamp center and 2D , the point of refraction at the EQ-SM interface, PREQ-SM,dir1 can also be calculated using the law of cosines: 2D )2] ⁄ Req,dir1,max ) arccos{[RL2 + (RL - tq)2 - (deq,dir1,max

[2RL(RL - tq)]} (3)

where Req,dir1,max is the maximum angle among PSmaxdir1, lamp center, and PREQ-SM,dir12D. The maximum angle among PSmaxdir1, lamp center and the RS, Rtotal,dir1,max can be calculated employing trigonometric relations for the right triangle and the calculated value for Req,dir1,max: Rtotal,dir1,max ) arccos[RL ⁄ (RL + DRS)] + Req,dir1,max

(4)

where DRS is the distance from the lamp surface to the receptor site. The arc length, ldir1,max, corresponding to Rtotal,dir1,max, can be calculated as ldir1,max ) RLRtotal,dir1,max

(5)

The total number of PSs that contribute radiation to a RS via the dir1 pathway from one side of the excimer lamp, PSjmaxdir1, can be found by dividing the total arc length, ldir1,max, by the chosen spacing distance between PSs, s, rounding down the results to the nearest whole number, and adding 1 to account for the PS positioned closest to the receptor site, PS0: PSjmaxdir1 ) ROUND DOWN(ldir1,max ⁄ s) + 1

(6)

The angle between two neighboring point sources and the lamp center, RPS, is a constant value and can be expressed as RPS ) s ⁄ RL

(7)

The next step in the SPACE model is to calculate the path length of radiation transmitted through the EQ envelope, 2D 2D , and the SM, dsm,dir1,j from the jth PS, PSj, to the ith deq,dir1,j RS, RSi. An example of this pathway is illustrated in Figure 6. Path length calculation is necessary so that the effects of absorbance by the quartz material and the SM can be accounted for, as well as the dissipation of radiation in space. 2D 2D and dsm,dir1,j , the point of To be able to calculate deq,dir1,j 2D , must be refraction at the EQ-SM interface, PREQ-SM,dir1 known. This point is determined through an iterative VOL. 42, NO. 5, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

1607

FIGURE 5. Illustration of the number and location point sources that contribute radiation to the ith receptor site via direct transmission through the exterior quartz envelope and the surrounding medium (dir1 pathway, two-dimensional representation).

FIGURE 6. Example of a dir1 radiation pathway through the exterior quartz envelope and the surrounding medium (two-dimensional representation). procedure, in which an initial guess is made for the angle among the PSj, lamp center, and PR2D EQ-SM,dir1, Req,dir,j. Iterations 1608

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 5, 2008

begin by calculating the relevant distances for the PS farthest from the RS and end with the point source directly beneath the

RS, that is, starting from the PS indexed with the highest digit, jmaxdir1, and continuing in the decreasing order until PS0. An example of the numeration of PSs is illustrated in Figure 5. The guess is made on the basis of the final value first guess for each Req,dir1,j final from the previous iteration. In the case of the first of Req,dir,j+1 iteration for point jmaxdir1, Rguess eq,dir1,jmaxdir1 is equal to the maximum value Req,dir1,max. guess final Req,dir1,j ) Req,dir1,j+1

(8)

guess where Req,dir1,j is the first guess for Req,dir1,j for point source j final and Req,dir1,j+1 is the final value for Req,dir1,j+1 for point source j + 1. The path lengths of radiation transmitted through the EQ 2D 2D , and the SM, dsm,dir1,j from PSj to the RS are envelope, deq,dir1,j calculated as follows. 2D is calculated using the law of cosines and the (1) dsm,dir1,j guess : first guess approximation for Req,dir,j

2D,iteration 1 dsm,dir1,j ) guess ] √(RL + DRS)2 + RL2 - 2(RL + DRS)RL cos[(j - 1)RPS-Req,dir1,j

(9)

(2) The angle of refraction at the EQ-SM interface, θ2D sm,dir1,j, is calculated on the basis of the law of cosines for its 2D : complementary angle, λsm,dir1,j iteration 1 2D,iteration 1 2 λsm,dir1,j ) arccos{[RL2 + (dsm,dir1,j )2D,iteration 1 )} ] ⁄ (2RLdsm,dir1,j

(RL + DRS)2 2D,iteration 1 iteration 1 θsm,dir1,j ) π - λsm,dir1,j

(10)

2D , is (3) The incident angle at the EQ-SM interface, θeq,dir1,j obtained according to Snell’s law:

2D,iteration 1 2D,iteration 1 ) arcsin[(nsm⁄nq) sin θsm,dir1,j θeq,dir1,j ]

(11)

(4) d2D eq,dir1,j is then calculated employing the law of cosines:

{

2D,iteration 1 2D,iteration 1 ) 0.5 2RL cos θeq,dir1,j deq,dir1,j

2D,iteration 1 2 ) - 4[RL2 - (RL - tq)2]} √(2RL cos θeq,dir1,j

(12)

(5) The final step of one iterative cycle is the computation of Req,dir1,j: iteration 1 2D,iteration 1 2 Req,dir1,j ) arccos {[(RL - tq)2 + RL2 - (deq,dir1,j ) ]⁄

[2RL(RL - tq)]}

(13)

The subsequent iteration starts with using the Req,dir1,j value 2D in the same from the previous iteration to compute dsm,dir1,j manner as presented in step 1 of the iteration cycle:

√(RL + DRS)

2D 2D,iteration n ) deq,dir1,j deq,dir1,j 2D 2D,iteration ) dsm,dir1,j dsm,dir1,j

n

(16)

2D,iteration n 2D,iteration n teq,dir1,j ) deq,dir1,j cos θeq,dir1,j 2D,iteration n 2D, iteration n tsm,dir1,j ) dsm,dir1,j cos θsm,dir1,j

Equations 1–16 can be used to simulate the contributions to the fluence rate received at a receptor site via the dir1 pathway in a cross-sectional plane of the reactor system. However, a model of the E′ distribution surrounding a cylindrical excimer lamp must account for the threedimensional (3D) nature of the lamp. Analogous to the iterative procedures used in 2D calculations, the objective of iterations performed as a part of the 3D analysis was to identify the location of the planes and points of refraction. The location of each point of refraction was defined by three-coordinate positions, x, y, and z. The x and y positions were identified in the 2D analysis. The methodology used to find the z (longitudinal) locations is presented below. The 3D analysis for the dir1 radiation pathway involves identification of one point of refraction at the EQ-SM 3D , for each PS. This point is illustrated in interface, PREQ-SM,dir1 Figure 7, along with other relevant variables used in 3D calculations of dir1 radiation pathways. For PSj, which is located a distance ∆ztotal,dir1,j from RSi, the longitudinal distance between the RS and PR3D EQ-SM,dir1 is marked as ∆zsm,dir1,j. A relatively simple iterative method is used to approximate ∆zsm,dir1,j and the distance between PSj and the plane of refraction, ∆zEQ,dir1,j, and to calculate the 3D radiation 3D 3D and dsm,dir1,j . pathways through the EQ and SM, deq,dir1,j Iterations for the jth PS start with an initial approximation that ∆zeq,dir1,j is equal to zero: guess ≈0 ∆zeq,dir1,j

(17)

guess ≈ ∆ztotal,dir1,j ∆zsm,dir1,j

The following iterative procedure is used to converge on 3D : the location of PREQ-SM,dir1 3D is calculated on the basis of trigonometric (1) dsm,dir1,j 3D , ∆zsm,dir1,j, relations for the right triangle formed by dsm,dir1,j 3D : and dsm,dir1,j 3D,iteration 1 2D guess dsm,dir1,j ) √(dsm,dir1,j )2 )2 + (∆zsm,dir1,j

2D, iteration 2 ) dsm, dir1,j 2

2D 2D and dsm,dir1,j , as well as their projections on the deq,dir1,j normal at the point of refraction at the EQ-SM interface, teq,dir1,j and tsm,dir1,j, respectively, are then also stored in the computer memory to be used in three-dimensional calculations:

+ RL2 - 2(RL + DRS)RLcos

iteration 1 (j - 1)RPS - Req, dir1, j

[

]

(14)

(18)

3D , is then calculated on (2) The angle of refraction, θsm,dir1,j the basis of trigonometric relations for the triangle marked 3D in Figure 7: Tsm,dir1,j

The values for all variables introduced in the each of the five steps of the iterative cycle are updated in subsequent iterations, and this process is continued until the absolute difference between Req,dir1,j values in two consecutive iterations is less than 10-6 and the Req,dir1,j value from the final performed iteration is then assigned as the final Req,dir1,j value final : for the jth point source, Req,dir1,j

(3) Snell’s law is applied to calculate the angle of incidence, 3D : θeq,dir1,j

iteration n iteration n-1 Req,dir1,j - Req,dir1,j < 10-6

(4) d3D eq,dir1,j is formulated on the basis of the triangle marked 3D in Figure 7: Teq,dir1,j

|

|

(15)

3D,iteration 1 3D,iteration 1 θsm,dir1,j ) arccos(tsm,dir1,j ⁄ dsm,dir1,j )

(19)

3D,iteration 1 3D,iteration 1 θeq,dir1,j ) arcsin[(nsm ⁄ nq) sin θsm,dir1,j ]

(20)

iteration n final Req,dir1,j ) Req,dir1,j

3D,iteration 1 3D,iteration 1 deq,dir1,j ) teq,dir1,j ⁄ cos θeq,dir1,j

where n is the number assigned to the final performed iteration before convergence.

(5) ∆zsm,dir1,j can next be calculated on the basis of known 2D 3D and deq,dir1,j : values for deq,dir1,j VOL. 42, NO. 5, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

(21)

9

1609

FIGURE 7. Schematic representation of a dir1 radiation pathway through the exterior quartz envelope and the surrounding medium (three-dimensional representation). iteration 1 3D,iteration 1 2 2D ∆zeq,dir1,j ) √(deq,dir1,j ) - (deq,dir1,j )2

(22)

(6) The final step of one iterative cycle is the computation of ∆zsm,dir1,j: iteration 1 iteration 1 ) ∆ztotal,dir1,j-∆zeq,dir1,j ∆zsm,dir1,j

(23)

The succeeding iterative cycle starts with step 1 using the computed value for ∆zsm,dir1,j from the previous iteration to 3D : compute dsm,dir1,j 3D,iteration 2 2D iteration 1 2 dsm,dir1,j ) √(dsm,dir1,j )2 + (∆zsm,dir1,j )

(24)

The iterative cycle is repeated until:

|

|

iteration n iteration n-1 ∆ztotal,dir1,j - (∆zeq,dir1,j + ∆zsm,dir1,j ) < 10-3

(25)

(26)

where REQ-SM,dir1,j is the reflectance at the EQ-SM interface for the dir1 radiation pathway, r⊥,EQ-SM,dir1,j is the amplitude of radiant energy from PSj perpendicular to the plane of incidence at the EQ-SM interface for the dir1 radiation pathway, and r|,EQ-SM,dir1,j is the amplitude of radiant energy 1610

9

r⊥,EQ-SM,dir1,j )

r|,EQ-SM,dir1,j )

3D,iteration n 3D,iteration n nq cos θeq,dir1,j -nsm cos θsm,dir1,j 3D,iteration n 3D,iteration n nq cos θeq,dir1,j +nsm cos θsm,dir1,j (27) 3D,iteration n 3D,iteration n nsm cos θeq,dir1,j -nq cos θsm,dir1,j 3D,iteration n 3D,iteration n nsm cos θeq,dir1,j +nq cos θsm,dir1,j

The final equation describing the fluence rate received at RSi from PSj is

2D 2D 3D , dsm,dir1,j , θeq,dir1,j , The attainment of values for deq,dir1,j 3D enables the formulation of the equation for and θsm,dir1,j the fluence rate seen at RSi from PSj via the dir1 radiation pathway. This equation accounts for dissipation of radiation in space according to the inverse square law, absorbance of radiation following Beer–Lambert’s law, and refraction and reflection of radiation transmitting through interfaces between media with different refractive indices, in accordance with Snell’s law and Fresnel’s law (16). At an interface between two media with different refractive indices, the ratio of reflected over incident flux is defined as reflectance and for reflection of dir1 radiation at the EQ-SM interface is mathematically equivalent to

2 2 +r|,EQ-SM,dir1,j REQ-SM,dir1,j ) 0.5(r⊥,EQ-SM,dir1,j )

from PSj parallel to the plane of incidence at the EQ-SM interface for the dir1 radiation pathway. Fresnel’s equations describe r⊥ and r| and are stated in terms of the angles of incidence and refraction and the indices of refraction:

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 5, 2008

E′dir1,j ) 3D,iteration n 3D,iteration n -σsmdsm,dir1,j ) Pj(1 - REQ-SM,dir1,j) exp(-σqdeq,dir1,j 3D,iteration n 3D,iteration n 2 4π(deq,dir1,j + dsm,dir1,j )

(28) where E′dir1,j is the fluence rate contribution at RSi from PSj via the dir1 radiation pathway (in milliwatts per square centimeter), Pj is the output power attributable to PSj (in milliwatts), σq is the absorbance coefficient of quartz (in inverse centimeters), and σsm is the absorbance coefficient of SM (in inverse centimeters). It should be noted that according to Snell’s law, if radiation is incident upon a medium with a lower index of refraction, as is the case at the EQ-SM interface when the SM is either air or water, there exists a critical angle of incidence above which all radiation will be reflected, and there will be no transmission of radiation at that interface. This phenomenon is called total internal reflection, and the critical incident angle at the EQ-SM 3D,crit , is defined by Snell’s law: interface, θeq,dir1,j π 3D 3D,crit ) nsm sin θsm,dir1,j ) nsm sin )nsm nq sin θeq,dir1,j 2

(29)

FIGURE 8. Experimental setup for actinometry experiments. 3D,crit θeq,dir1,j )arcsin(nsm ⁄ nq) 3D 3D,crit , E′ is greater than θeq,dir1,j If the incident angle θeq,dir1,j dir1,j from PSj is equal to zero. Collectively, eqs 1–29 represent the algorithm used to simulate radiation delivered to a receptor site via the dir1 pathway. Conceptually similar algorithms were developed for the dir2, internal reflection, and reflection off reactor housing pathways. Details of the development of these algorithms are presented in the Supporting Information. Experimental Methods: SPACE Model Validation by Local Actinometry. The SPACE model was applied to simulate the E′ distribution around a XeBr* lamp, and the fluence rate predictions were compared to measurements made with an iodide/iodate actinometer at four different distances from the excimer lamp. The experimental setup is illustrated in schematic form in Figure 8. The excimer lamp had an external diameter of 5.0 cm, and the active length was 25 cm, defined by the portion of the lamp covered with a metal mesh that acted as a grounding electrode. The excimer gas gap was 1.0 cm, and the thickness of the quartz envelopes was 1.0 mm. The surrounding medium was air. The aqueous actinometer solution was pumped through a quartz capillary tube (CT) at a constant flow rate of 30.5 mL/min. The CT had an external diameter of 5 mm and an internal diameter of 3 mm (i.e., wall thickness of 1 mm). The CT was positioned 0.14, 1.14, 2.14, and 5.54 cm from the surface of the excimer lamp, with the CT axis being oriented parallel to the axis of the lamp. The total energy absorbed by the actinometer solution was quantified by measuring the level of triiodide production that resulted from exposure of the actinometer

to UV radiation, as defined by the following overall stoichiometric expression (17, 18): 8I- + IO3 + 3H2O + hv ) 3I3 + 6OH

(30)

The iodide/iodate actinometer solution was generated by mixing aqueous solutions of potassium iodide and potassium iodate prepared using a sodium borate/phosphate buffer (pH 9.25) to produce 0.6 M potassium iodide and 0.1 M potassium iodate. The solution was stored in the dark until use. Fresh actinometer solutions were prepared daily. All actinometer experiments were performed at room temperature (approximately 25 °C). As illustrated in eq 30, iodide, when exposed to UV radiation in the presence of an electron scavenger such as iodate, is converted to triiodide (I3-). Triiodide has a large molar absorptivity at 352 nm and can therefore be easily detected with a spectrophotometer. The molar absorptivity used for this study was 27600 M-1 cm-1, as determined by Rahn et al. (18). Following irradiation, the photoreacted iodide/iodate solution was transferred to a quartz spectrophotometric cell with a path length of 1 cm. The absorbance of the solution was measured at 352 nm (Cary 900 UV–vis) and correlated to triiodide concentration using Beer’s law. A flat-plate collimator was used during the experiments to aid in the measurement of lamp output, in conjunction with an International Light model IL1700 radiometer with a model SED240 planar detector. The radiometer/detector was calibrated by the manufacturer to allow direct measurement of the incident fluence rate at 282 nm. The measured fluence VOL. 42, NO. 5, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

1611

FIGURE 9. Production of triiodide as a function of distance from the excimer lamp.

FIGURE 10. Linear regression fit between the amount of triiodide measured experimentally and predicted numerically. rate values were used to calculate the lamp output power used in the E′ distribution representations with the SPACE model. A numerical approach developed by Shen (19) was adapted to compute the total amount of energy absorbed by the actinometer solution. This approach accounts for the geometry and positioning of the excimer lamp and the actinometer tube that determined the number of point sources contributing radiation absorbed by the actinometer, as well as for the reflection, refraction, and absorbance effects of the excimer lamp and actinometer capillary tube quartz walls, the surrounding media, and the actinometer solution. Computation of the energy absorbed by the actinometer solution is presented in detail in the Supporting Information. Input parameters used in this model were measured or calculated for 282 nm and included the absorbance coefficients of the excimer lamp quartz walls and the quartz capillary tube, and the indices of refraction for quartz, the aluminum internal electrode, air, excimer gas, and the actinometer solution. Parameter values used in the model 1612

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 5, 2008

are presented in Table 1. Quartz capillary tube transmittance measurements are described in the Supporting Information. The refractive index of the aluminum internal electrode was measured using a sample of the material obtained from the manufacturer of the excimer lamp, Ushio America Inc. Reflection at 282 nm and 45° off the aluminum sample was measured with a spectrometer (model USB 2000, Ocean Optics Inc., Dunedin, FL), and the refractive index of 51 was calculated from the measured reflectivity value of 92.1%. The total lamp output power was estimated on the basis of fluence rate measurements of collimated radiation from the excimer lamp with a radiometer (model IL 1700, International Light Inc., Newburyport, MA) with a model SED240 detector, positioned 2 cm from the edge of the collimator, as depicted in Figure 8. An inverse form of the SPACE model was used to back-calculate the lamp output power from the fluence rate measurement of 80.2 µW/cm2 (see the Supporting Information for calculation details). The spectrophotometric measurements of triiodide production resulting from UV exposure were compared to the

TABLE 1.

Input Parameters for Computation of the Energy Absorbed by the Actinometer Solution at 282 nm parameter

value cm-1

quartz lamp wall absorbance coefficient quartz capillary tube absorbance coefficient refractive index of quartz refractive index of aluminum refractive index of air refractive index of excimer gas refractive index of actinometer solution

0.85 1.29 cm-1 1.497 50.985 1.00029 1.00029 1.365

TABLE 2.

Total Amount of Energy Absorbed by the Actinometer as a Function of Distance from the Excimer Lamp and Fractional Contributions via Different Radiation Pathways energy (mJ) DCT-LS (cm) total 0.14 1.14 2.14 5.54

8.73 7.16 5.85 3.24

fraction of total energy (%)

DIR1

DIR2

IER

DIR1

DIR2

IER

4.25 3.48 2.80 1.57

1.94 1.54 1.27 0.68

2.55 2.14 1.78 0.99

48.6 48.6 47.9 48.4

22.2 21.5 21.8 21.0

29.2 29.9 30.3 30.6

amount of triiodide production predicted by numerical modeling. The numerical model yielded an estimate of the total energy absorbed by the actinometer, and this value was correlated to the number of moles of triiodide produced based on the quantum yield (for radiation with λ ) 282 nm) for the iodate/iodide actinometer of 0.41 mol/einstein. A discussion of the experiments that were performed to determine the quantum yield is summarized in the Supporting Information. It should be noted that the quantum yield measured as part of this research was larger than the values previously reported by Rahn et al. (18).

Results and Discussion The results of the actinometry experiments are plotted in Figure 9 as the number of moles of triiodide produced as a function of the distance from the capillary tube surface to the excimer lamp surface. The quantity of triiodide produced as predicted by numerical calculations is also presented in Figure 9. A linear correlation between the numerical predictions and experimentally measured values of triiodide production is presented in Figure 10. The value of 1.05 for the slope indicates good agreement between the experimental and numerical data. This method of analysis also reveals the total amount of energy absorbed by the actinometer and fractional contributions via different radiation pathways at different distances of the CT from the lamp surface. A summary of this analysis is presented in Table 2. Apparently, the fractional contributions from all three radiation pathways were important to the total fluence rate received by the actinometer solution at these four locations in the system. The pathway that accounts for reflection off the external housing was not relevant in the local actinometry experiments or the numerical simulations that were performed to simulate these experiments, as the reactor housing used in the experimental setup depicted in Figure 8 was covered with a nonreflective black cloth. The results of the measurements and simulations that are summarized in Figures 9 and 10, as well as in Table 2, suggest that all radiation pathways described in this model provide relevant contributions to the fluence rate transmitted to a receptor site and that, in general, none of these pathways can be ignored.

source 20 measured 21 measured 22-24 22-24 25

Acknowledgments This work was funded by the NASA Specialized Center for Research and Training. Excimer lamps were made available by Ushio America, Inc.

Supporting Information Available Details on the principles of excimer formation and radiation emission, calculations for the direct and reflection pathways, computations of the total energy absorbed by an actinometer solution when exposed to UV radiation from an excimer lamp, description of experiments conducted to determine the iodide/iodate actinometer quantum yield, quartz capillary tube transmittance measurements, excimer lamp output power calculations, and examples of fluence rate distribution profiles as computed by the SPACE model. This information is available free of charge via the Internet at http:// pubs.acs.org.

Literature Cited (1) Chiu, K.; Lyn, D. A.; Savoye, P.; Blatchley, E. R., III. Integrated UV disinfection model based on particle tracking. J. Environ. Eng. Div. (Am. Soc. Civ. Eng.) 1999, 125 (1), 7–16. (2) Lyn, D. A.; Chiu, K.; Blatchley, E. R., III. Numerical modelling of flow and disinfection in UV disinfection channels. J. Environ. Eng. (Reston, VA, U.S.) 1999, 125 (1), 17–26. (3) Lyn, D. A. Steady and unsteady simulations of turbulent flow and transport in ultraviolet disinfection channels. Journal of Hydraulic Engineering 2004, 130 (8), 762–770. (4) Lyn, D. A.; Blatchley, E. R., III. Numerical computation fluid dynamics-based models of ultraviolet disinfection channels. J. Environ. Eng. (Reston, VA, U.S.) 2005, 131 (6), 838–850. (5) Blatchley, E. R., III. Numerical modelling of UV intensity: Application to collimated beam reactors and continuous-flow systems. Water Res. 1997, 31 (9), 2205–2218. (6) Bolton, J. R. Calculations of ultraviolet fluence rate distributions in an annular reactor: Significance of refraction and reflection. Water Res. 2000, 34 (13), 3315–3324. (7) Pennell, K.; Naunovic, Z.; Blatchley, E. R., III. Effect of sequential disinfection on Bacillus subtilis spores using ultraviolet irradiation and iodination. Proceedings of WQTC; Quebec City, QC, Canada, 2005. (8) Giese, N.; Darby, J. Sensitivity of microorganisms to different wavelengths of UV light: Implication on modeling of medium pressure UV systems. Water Res. 2000, 34 (16), 4007–4013. (9) Sosnin, E. A.; Lavrent’eva, L. V.; Erofeev, M. V.; Masterova, Y. V.; Kuznetzova, E. N.; Tarasenko, V. F. A new bactericidal UV light source: Excilamps. Proc. SPIE 2004, 5483, 317–322. (10) Naunovic, Z.; Pennell, K.; Lyn, D. A.; Blatchley, E. R., III. Design and testing of a UV disinfection system based on non-mercury containing lamps. Proceedings of WQTC; Denver, 2006. (11) Kogelschatz, U. Silent discharges for the generation of ultraviolet and vacuum ultraviolet excimer radiation. Pure Appl. Chem. 1990, 62 (9), 1667–1674. (12) Zhang, J. Y.; Boyd, I. W. Efficient XeI* excimer ultraviolet sources from a dielectric barrier discharge. J. Appl. Phys. 1998, 84 (3), 1174–1178. (13) Kogelschatz, U. Filamentary, patterned, and diffuse barrier discharges. IEEE Trans. Plasma Sci. 2002, 30 (4), 1400–1408. (14) Coogan, J. Pathogen control in complex fluids using watercoupled excimer lamps at 282 and 308 nm. J. Photochem. Photobiol. 2005, 81, 1511–1517. (15) Gellert, B. UV generation in dielectric barrier discharges. Contr. Plasma Phys. 1991, 31 (2), 247–259. VOL. 42, NO. 5, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

9

1613

(16) Meyer-Ardent, J. R. Introduction to classical and modern optics; Prentice-Hall: Englewood Cliffs, NJ, 1984. (17) Rahn, R. O. Potassium iodide as a chemical actinometer for 254 nm radiation: Use of iodate as an electron scavenger. J. Photochem. Photobiol. 1997, 66 (4), 450–455. (18) Rahn, R. O.; Stefan, M. I.; Bolton, J. R.; Goren, E.; Shaw, P.-S.; Lykke, K. R. Quantum yield of the iodide-iodate chemical actinometer: Dependence on wavelength and concentration. J. Photochem. Photobiol. 2003, 78 (2), 146–152. (19) Shen, C. Characterization of UV irradiance field in UV disinfection systems by local actinometry. Ph.D. Dissertation, Purdue University, West Lafayette, IN, 2004. (20) General Electric Company Transmission Calculator. http:// www.gequartz.com/en/tools/trans/transmission.htm. (21) Rodney, W. S.; Spindler, R. J. Index of refraction of fused quartz for ultraviolet, visible, and infrared wavelengths. J. Opt. Soc. Am. 1954, 44, 677–679.

1614

9

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 42, NO. 5, 2008

(22) Shen, C.; Fang, S.; Bergstrom, D. E.; Blatchley, E. R. (E)-5-[2(Methoxycarbonyl)ethenyl]cytidine as a chemical actinometer for germicidal UV radiation. Environ. Sci. Technol. 2005, 39 (10), 3826–3832. (23) Edlen, B. The refractive index of air. Metrologia 1966, 2 (2), 71–80. (24) Schiebener, P.; Straub, J.; Levelt Sengers, J. M. H.; Gallagher, J. S. Refractive index of water and steam as function of wavelength, temperature and density. J. Phys. Chem. Ref. Data 1990, 19 (3), 677–717. (25) International Association for the Properties of Water and Steam. Release on the refractive index of ordinary water substance as a function of wavelength, temperature and pressure; Erlangen, Germany, 1997.

ES070968W