Ray Tracing for Fluence Rate Simulations in Ultraviolet Photoreactors

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Remediation and Control Technologies

Raytracing for Fluence Rate Simulations in Ultraviolet Photoreactors Yousra M. Ahmed, Mark Jongewaard, Mengkai Li, and Ernest R. Blatchley Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b06250 • Publication Date (Web): 29 Mar 2018 Downloaded from http://pubs.acs.org on March 31, 2018

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Environmental Science & Technology

Raytracing for Fluence Rate Simulations in Ultraviolet Photoreactors

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Yousra M. Ahmed†, Mark Jongewaard‡, Mengkai Li†§,, Ernest R. Blatchley III*, †∥

3 4 5

†

6

States;

7

‡

8

§

9

Environmental Sciences, Chinese Academy of Sciences, 18 Shuang-qing Road, Beijing 100085,

Lyles School of Civil Engineering, Purdue University, West Lafayette, Indiana 47907, United

LTI Optics, LLC, Westminster, Colorado 80021, United States; Laboratory of Drinking Water Science and Technology, Research Center for Eco-

10

China;

11

∥

12

Indiana 47907, United States;

Division of Environmental & Ecological Engineering, Purdue University, West Lafayette,

13 14

*

15

[email protected]; Lyles School of Civil Engineering, Purdue University, 550 Stadium

16

Mall Drive, West Lafayette, IN 47907 USA

Corresponding author: ph. 1-765-494-0316; fax 1-765-494-0395; email

17 18

ABSTRACT: The performance of photochemical reactors is governed by the spatial

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distribution of radiant energy within the irradiated region of the reactor. Raytracing has

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been widely used for simulation of lighting systems. The central hypothesis of this work

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was that raytracing can provide accurate simulations of fluence rate fields within

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ultraviolet (UV) photoreactors by accounting for the physical and optical phenomena that

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will govern fluence rate fields in UV photoreactors. Raytracing works by simulating the

ACS Paragon Plus Environment


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behavior of a large population of rays emanating from a radiation source to describe the

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spatial distribution of radiant energy (i.e., fluence rate) within a system. In this study,

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fluence rate calculations were performed using commercial raytracing software for three

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basic UV reactors, each with a single low-pressure Hg lamp. Fluence rate calculations in

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the raytracing program were based on the formal definition of fluence rate, calculated as

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the incident radiant power from all directions on a small spherical receptor, divided by

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the cross-sectional area of that sphere.

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raytracing can provide predictions of fluence rate in UV radiative systems that are close

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to experimental measurements and the predictions of other numerical methods.

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Key words: Raytracing; ultraviolet; fluence rate; photo-reactors.

The results of this study demonstrate that

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■ INTRODUCTION

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The Ultraviolet (UV) spectrum spans the wavelength range from 100-400 nm. This

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spectrum has been sub-divided into four ranges that comprise vacuum UV radiation (100-

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200 nm); UVC, often referred to as germicidal UV (200-280 nm); UVB (280-315 nm);

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and UVA (315-400 nm). Disinfection applications generally involve UVC radiation due

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to strong absorbance among nucleic acids and other biomolecules, especially in the

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wavelength range of 250-270 nm,1 but UVB and UVA radiation also demonstrate

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germicidal behavior.2,3 UV photoreactors are also commonly applied to accomplish

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direct photolysis or as part of an advanced oxidation process.

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The most common terms used to quantify the spatial distribution of radiant energy of

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UV radiation in UV photoreactors are irradiance (E) and fluence rate (Eo). Irradiance is


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defined as the total radiant power on an element surface from all upward directions,

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divided by the area of that element, expressed in units of power per unit area (e.g.,

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mW/cm²).4 Fluence rate (Eo) is a more general term used to quantify incident UV

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exposure and is defined as the total radiant power incident on an infinitesimally-small

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sphere from all directions divided by its cross-sectional area, also expressed in units of

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power per unit area.4 In the special case of a perfectly collimated UV source incident

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perpendicular to a plane, E and Eo are identical.4

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The local rate of a photochemical reaction is directly proportional to the local fluence

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rate. More generally, process performance of photoreactors is governed by the “dose”

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(fluence) of UV radiation received by the photochemical targets (expressed in energy per

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unit area, e.g., mJ/cm2). The UV dose received by a waterborne/airborne target in a UV

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photoreactor is influenced by exposure time and the fluence rate history of the target. In

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turn, these parameters are influenced by the geometry of the reactor system, type and

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location of the UV sources, and the optical characteristics of the media that comprise the

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system.5 Integration of the fluence rate field with the fluid mechanical behavior of the

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system allows estimation of the fluence (dose) distribution delivered by the reactor.6

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Detailed, accurate simulations of fluid mechanics in photochemical reactors can be

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accomplished through the application of computational fluid dynamics (CFD). Similarly,

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accurate and detailed simulations of the fluence rate field could yield improvements in

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the ability to predict the performance of UV photoreactors.

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A common germicidal UV radiation source is a low-pressure (LP) mercury vapor

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lamp, which emits most of its ultraviolet radiation at 254 nm, close to the optimal

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wavelength for disinfection. For water treatment systems, LP lamps are usually housed



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in a quartz glass sleeve inside the reactor chamber to prevent direct contact of the lamp

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and its electrical components with water, while allowing most of the UV radiation

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generated by the lamp to be transmitted to the surrounding fluid. UV radiation emitted

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from the lamp encounters numerous components within the system including the lamp

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envelope, air in the annular space between the lamp and the surrounding quartz sleeve,

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the quartz sleeve, water, other lamps, and the reactor walls (Figure S1). Each of these

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system components is characterized by quantifiable optical attributes, all of which will

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affect the spatial distribution of radiant energy (i.e., fluence rate field).

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Fluence rate field predictions and measurements. Over the last three decades,

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several numerical models have been developed to simulate Eo distributions inside UV

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photoreactors. Among the most common models is point source summation (PSS).7 An

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integrated form of the PSS model over an infinite number of point sources was later

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introduced by Blatchley8 as the line source integration (LSI) model. These models

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provide inaccurate estimates of fluence rate in the near-field (i.e., close to the radiation

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source) because of the simplified geometry they represent, and because they do not

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account for the effects of reflection or refraction. Bolton introduced the multiple segment

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source summation (MSSS) model that incorporated much of the PSS model, in which the

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lamp was modeled as a series of differential cylindrical segments where the radiation was

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emitted normal to the cylinder surface and decreased as a cosine function with the angle

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of beam emission.9,10 The commercial software UVCalc3D (Bolton Photosciences Inc.,

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Edmonton, AB, Canada), which is based on the MSSS model and includes terms to

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account for the effects of reflection and refraction, has been applied for simulating the

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fluence rate distributions in UV reactors. The MSSS model also accounts for the spectral


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output of the lamp and absorbance of the surrounding fluid medium. Other numerical

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approaches aimed at modeling the E0 field around Hg lamps include the Extensive Source

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Volumetric Emission (ESVE) and Extensive Source with Superficial Diffuse Emission

95

(ESDE) models.11,12 In the ESVE model, it is assumed that point emitters are uniformly

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distributed within the lamp volume that emit isotropically. The ESDE model assumes

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that radiation is emitted in a diffuse manner by point sources that are uniformly

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distributed within the lamp volume.

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The Discrete Ordinate (DO), finite volume, and Monte Carlo methods represent three

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different approaches for solving the radiative heat transfer equation (RTE).13 The RTE

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describes the propagation of radiation through homogeneous or heterogeneous media by

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accounting for absorption, emission, and scattering behavior.

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The limitations of the numerical fluence rate models described above motivated

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exploration of raytracing as a tool for simulation of fluence rate fields in UV

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photoreactors.

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from one or more sources as a large number of individual rays; the fate of radiant energy

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along the path of each ray can be accurately simulated using the fundamental laws of

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optics, including those that govern refraction, reflection, absorbance, and shadowing.

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Raytracing has previously been applied by Lau et al.14 to simulate the UV fluence rate

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field in an in-duct UVGI system of an HVAC system. Lau et al. modeled a HVAC UV

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system and predicted UV irradiance within a test rig of three UV lamps within the

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irradiated air medium. They defined two irradiance terms: planar irradiance and spherical

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irradiance. Lau et al. predicted spherical irradiance by dividing the incident radiation on

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spherical receptors (2.54 cm diameter) by the total area of sphere, and planar irradiance

Raytracing simulates the behavior of electromagnetic radiation emitted



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by predicting the incident radiation on a planar surface area. However, neither of these

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quantities represent the true value of fluence rate, which is the relevant parameter for

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most photochemical reactor systems.

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The primary objective of this paper was to examine the ability of the raytracing

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approach to provide reliable, accurate predictions of Eo in UV systems that are applied in

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water treatment. The results of raytracing calculations were compared to other physical,

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numerical, and chemical methods.

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Direct measurements of fluence rate are necessary to validate simulation models.

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UV radiometers and chemical actinometers are the most common experimental methods

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for performing irradiance/fluence rate measurements.8,15 An experimental method of

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particular interest in this work was the method sometimes referred to as spherical

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actinometry, wherein a chemical actinometer, such as iodide/iodate, is enclosed in one or

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more small, spherical quartz vessels.16,

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formal definition of fluence rate, in that it accounts for radiation power imposed on a

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small, spherical photon receptor from all directions. However, conventional radiometry

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and actinometry both fail in close proximity to radiation sources because of geometric

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restrictions and the variable response of radiometers to off-angle (i.e., non-perpendicular)

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radiation, as well as the risk of saturation of the actinometer solution under high fluence

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rate.12 In addition, the effects of reflection and refraction may be important in spherical

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actinometry experiments.

17

This approach was developed to mimic the

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The micro fluorescent silica detector (MFSD) of Li et al. represents an alternative to

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conventional radiometry and actinometry.18 The small size of this detector (1 mm long

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and 0.3 mm o.d.) and its ability to accept incident photons from virtually all angles allows


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it to accurately measure Eo at essentially any location in a UV photoreactor, including

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near-source regions such as the gap between the lamp and the sleeve. The MFSD has

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been used successfully to examine in-situ, real-time Eo distributions in reactors with

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single or multiple LP lamps in different media and with a wide range of UV

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transmittance.19 It has also been used to measure photon fluence rate distributions in

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photoreactors with polychromatic UV sources (e.g., medium-pressure Hg lamps).20

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For the work described herein, raytracing was applied to simulate fluence rate fields

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for several single-lamp UV photoreactors. The results of raytracing simulations were

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then compared with existing numerical and experimental results to evaluate its usefulness

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as a fluence rate calculation method.

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■ METHODS AND MATERIALS

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Raytracing simulations in this work were conducted using the commercial software

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Photopia (V2015, LTI Optics, Westminster, Colorado, USA).

Photopia uses a 3D

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probabilistic raytracing approach to predict the location and direction of ray emanation,

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and the direction of reflected and transmitted rays. The raytracing method involves

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digital definition of the physical boundaries of a system, as well as the physical (optical)

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characteristics of the system components.

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population of rays, it is possible to accurately describe the distribution of radiant energy

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within the system.

By simulating the behavior of a large

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Photopia includes a built-in CAD system that allows the user to create and

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manipulate source geometry, as well as the geometry of other system components with

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which radiation will “react.” Physical (optical) properties of the source and other system

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components are user-assigned.



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UV radiation modeling in Photopia. Low-pressure mercury (LP Hg) lamps are

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produced from quartz tubes with no internal fluorescent coating. Figure 1 illustrates the

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interactions of rays with other materials in the model that result from a single ray. As

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shown, rays emanating from the UV arc within the Hg lamp encounter refraction/Fresnel

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reflection reactions through the inner and outer surfaces of the lamp, the air/quartz (i.e.,

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inner) surface of the sleeve, and through the quartz/water (i.e., outer) surface of the

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sleeve. All lamps were assumed to emit radiation uniformly throughout the length of the

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lamp arc; the assumption of uniform emission was based on photographic images of

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output radiation from operating LP Hg lamps (see Figure S10-a).

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Refractive surfaces in the simulated system (e.g., quartz, water, and air interfaces)

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included inner and outer surfaces (i.e., front and back) and were defined by specifying the

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indices of refraction on both sides of each refractive surface, along with the material's

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extinction coefficient. Transmissive materials were assigned properties that allowed

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transmission either by allowing radiation to pass through without changing its direction,

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or scattering based on a measured bi-directional transmittance distribution function

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(BTDF). Clear glass is an example of a transmissive layer for visible light. To allow

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accounting for shadowing effects in the raytracing simulation, rays were blocked by

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shadowing surfaces in the lamp model (e.g., support structures), thereby forcing these

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rays to find a new emanation point.

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Most fluence rate numerical models do not explicitly model the UV lamp arc; for

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instance, the DO model does not include the lamp geometry, the air annulus, nor the

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thickness of the quartz sleeve. Instead it simply considers the radiation from the sleeve

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outer surface. UVCalc® approximates the UV lamp as a linear array of cylindrical


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segments emitting UV radiation from their edges. Although interaction of rays through

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the quartz sleeve surface (i.e., air/quartz/water interface) is accounted for in the model, it

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disregards the actual dimensions and physical features of the lamp.

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Different approaches can be employed to simulate the emission of rays from a UV

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source; to choose the most accurate representation of radiation emission, the effect of the

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emission mechanism on the fluence rate field predictions was examined by the raytracing

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model by comparing fluence rate predictions of three different emission patterns to

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experimental measurements. Based on this examination, which is explained in more

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detail in the SI (Section 2), it was observed that emission of rays starting from an arc

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surface inside an actual lamp yielded the closest estimates to the measurements.

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Spherical representation of fluence rate. Local fluence rate was calculated by

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dividing all incident radiant power on a small receptor sphere by the cross-sectional area

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of the sphere. The receiving sphere needs to be small enough to accurately represent the

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physical interpretation of local fluence rate; however, small spheres require relatively

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large numbers of rays to ensure interaction with the rays and good resolution and stability

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of the probabilistic raytracing solution, hence requiring more computational time.

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Therefore, sphere size was optimized to yield a stable, converged solution within a

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reasonable computational time. Figure S4 illustrates a radial array of spheres of 1 mm

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diameter arranged around a UV lamp. Fluence rate values at intermediate locations were

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estimated by linear interpolation. The effect of choosing a different sphere size (i.e.,

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radius) on Eo predictions at several locations from the raytracing simulations only caused

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up to 10% difference, so a subjective decision was made to use a sphere diameter of 1

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mm in the raytracing calculations (Figure S5).



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Raytracing parameters. Convergence on a stable fluence rate field calculation

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depends on the use of an appropriate number of rays emanated from the source.

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Raytracing solutions typically converge on a stable distribution as the number of rays

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increase. The number of rays required to converge on a stable solution depends on the

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number of lamps (radiation sources) in the model, as well as the size and geometry of the

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computational domain. The effect of changing the number of rays on the uniformity of

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the fluence rate calculations around a single UV lamp is illustrated in Figure 2 and

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discussed in the SI (Section 4).

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Figure 1. Ray paths resulting from a single ray that originates inside a LP Hg lamp,

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surrounded by a quartz jacket.

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2

Fluence Rate (W/cm )

300

250

200

150 106 rays 100

107 rays 5 x 107 rays 108 rays

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5 x 108 rays 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

219 220

Sphere Number Figure 2. Fluence rate around a single low-pressure Hg lamp as a function of number of

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rays emitted. Each data curve was obtained at a different number of rays ranging from

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106 to 5 x 108. The horizontal axis represents a numerical label (1-16) for sixteen

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spherical receptors that were distributed radially around the lamp at a fixed distance of 15

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mm from the center of the lamp.

225 226

Fluence rate calculations in water test reactor. Raytracing simulations were

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carried out for a single-lamp UV reactor filled with water with a UV transmittance of

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88% (based on a 1.0 cm optical path), as illustrated in Figure S6.

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measurements and numerical modeling for this reactor were performed by Liu et al.10 as

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part of their evaluation of commonly used fluence rate numerical models including

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MSSS, UVCalc3D, RAD-LSI, DO, and the View Factor Models. Liu et al.10 also used a


Fluence rate


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KI/KIO3 actinometer to measure fluence rate at specific locations in the water reactor by

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encasing the actinometer solution in small, quartz spheres.

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actinometer spheres are listed in Table S3.

The locations for the

235 (a)

(b)

236 (c)

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Figure 3. 2D view of the CAD model in Photopia for (a) the water test reactor of Liu et

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al.,10 (b) the glass reactor with single LP UV lamp of Li et al.,18 and (c) the annular

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reactor of Duran etal.12 constructed for raytracing simulations.

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The dimensions of the LP UV lamp used in this study were 28 cm length and 15 mm

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outer diameter. The thickness of the lamp envelope was assumed to be 1 mm; the total

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output power of the lamp at 254 nm was 16 watts. For the raytracing simulation,

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transmissive spheres were positioned at the same locations as the actinometer spheres

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(see Figure 3-a).

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UVCalc3D, RAD-LSI, and DO models, and measurements by the KI/KIO3 actinometer.

Raytracing simulation results were compared to those of the

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Fluence rate calculations in annular photo-reactor. Duran et al.12 applied finite

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volume (FV) based models to predict near-field and far-field fluence rate profiles for a

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single-phase annular reactor.

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fluence rate field for this same reactor; the output results from the raytracing analysis

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were compared to the experimental measurements (i.e., actinometers) and numerical

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model simulation results based on linear and extensive source models. UV transmittance

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of the water medium circulated inside the annular reactor was 98% (based on a 1.0 cm

255

optical path). Duran et al. applied linear source and extensive source emission models

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with isotropic or diffuse radiation (i.e., LSDE, LSSE, ESDE, and ESVE) to solve the

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radiative transfer equation (RTE) in connection with finite volume CFD simulations.12 In

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addition, a modified ESVE model was developed to include reflection/refraction and

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absorption of radiation at the air/quartz/water interface, as well as the absorption and re-

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emission of photons by the lamp plasma (abbreviated as: ESVERA).12 Fluence rate

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estimates from these numerical models were validated with experimental measurements

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using the potassium ferrioxalate actinometer for the near field irradiance at the reactor

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outer tube wall.

A raytracing simulation was conducted to predict the



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Figure S7 illustrates the actual geometry of the annular reactor used by Duran et al.,12

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while Figure 3-c illustrates the CAD model that was built for the raytracing simulation.

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Some components of the system were not included in the raytracing model for simplicity,

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since they were assumed to have negligible impact on the fluence rate predictions. These

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included the PVC jacket and the electrical tape. The rubber stoppers were included as a

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black (opaque) surface ends with zero reflection.

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Fluence rate calculations in glass reactor. The MFSD can capture radiation from

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essentially all angles with high sensitivity and can be used to measure Eo

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experimentally.18 The MFSD is a Ge-doped silica cylinder that is 1 mm long and 0.3 mm

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wide. Li et al.18 used this detector to measure Eo in a single LP UV lamp glass reactor,

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operating with air (100% UV transmittance) and water with 85% and 95% UV

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transmittance (based on a 1.0 cm path length). Axial Eo profiles were measured along the

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lamp with the MFSD at four radial distances (r) from the sleeve (r = 3, 8, 18, 28 cm) and

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were numerically predicted using UVCalc3D.

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The raytracing approach was used to re-calculate fluence rate profiles for the reactor

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configuration described by Li et al.18 to allow comparisons with the MFSD measurements

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and UVCalc3D predictions. The raytracing simulations included a UV lamp arc centered

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inside a quartz envelope and housed in a quartz sleeve in the middle of a glass reactor.

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The physical dimensions of all refractive surfaces were included; refractive indices (n) of

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1.51, 1.38, and 1.00 at 254 nm were assigned for quartz, water, and air, respectively.21, 22

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The reactor was open to air, so the effect of the air/water interface was accounted for.

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Figures S8 and S3-b illustrate the actual design of the reactor and its corresponding CAD

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schematic for the raytracing analysis, respectively.


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■ RESULTS AND DISCUSSION

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Water test reactor. Figure 4 displays the raytracing fluence rate predictions at

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several locations based on the DO, UVCalc3D, and RAD-LSI numerical model results,

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along with measurements by local actinometry.

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observed between the results of raytracing and experimental measurements at most

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locations than the other numerical models. At most locations (1, 2, 4, 5, 7, 9, 10, 12, and

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13) the raytracing results were closer to the actinometry measurements compared to other

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models, except some points like 3, 6, 8, 11, and 14. Locations of 3, 6, 8, and 11 are

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almost at the same X and Y distance from the lamp center, and close to the top and

296

bottom of the reactor. It was not clear from Liu’s study what material was present at the

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top and the bottom of the water test reactor. For the raytracing simulation, a reflective

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surface was assigned to the top and the bottom; therefore, there was a contribution of

299

reflection/refraction at these locations which might me be not have been present in the

300

actual system.

Generally, better agreement was

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It was noted that points 1, 2, 4, and 5 are the closest points to the reactor wall where

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the reflection effects tend to be most dominant; this explains why the raytracing

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predictions and the experimental measurements were notably higher than UVCalc, RAD-

304

LSI, and DO, since these models didn’t account for wall reflection. Moreover, Points 12,

305

13, and 14 are the closest points to the lamp and oftentimes it is mentioned in literature

306

that actinometry vessels might oversaturate in the close vicinity of the lamp and in this

307

case the measured fluence rate by the actinometer is lower than it should be. 12

308

A potential source of error in the experimental measurements with the actinometer

309

could be that the actinometer spherical vessels do not perfectly mimic the fluence rate



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definitions. This is because actinometer spheres have a diameter that is substantially

311

larger than that of the receiving spheres used in the raytracing simulations.

312

reflection/refraction attributes of the quartz spheres will influence the behavior of UV

313

radiation at the quartz-water interfaces of the spheres. Given the errors associated with

314

the experimental measurements as were reported by Liu et al.10 which are indicated by

315

error bars in Figure 4, the results indicate potential advantages of raytracing for fluence

316

rate field modeling in UV photoreactors, relative to other modeling approaches.

Also,

9 DO UVCALC3D RAD-LSI Raytracing Actinometry

8

2

Fluence Rate (mW/cm )

7 6 5 4 3 2 1 0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

317 318

Test Point Figure 4. Fluence rate values at test points, as calculated by DO, UVCalc3, RAD-LSI,

319

and raytracing, along with local (spherical) actinometry measurements. Error bars on

320

measurements represent standard deviation.

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Annular photo-reactor. Figure 5 illustrates the axial fluence rate profiles at the

323

outer tube surface of the annular reactor. The predictions of the FV numerical models

324

were comparable to each other and relatively close to the experimental measurements,

325

with some noticeable differences towards the ends regions of the tube, which showed a

326

steep decrease in fluence rate. Raytracing predictions of Eo followed the same pattern as

327

the other numerical models and were similar to measurements reported by the authors.12

328

The raytracing simulation over-predicted the fluence rate in the region 12 cm < axial

329

position < 15 cm by about 5-25% relative to the actinometry measurements; however,

330

they still fell within the experimental error margins, as did the ESVERA model results,

331

which also accounted for reflection, refraction, and absorption of the lamp quartz

332

envelope, as well as the absorption/remission for the Hg plasma of the lamp.

333

The ability of these numerical models, including raytracing, to predict Eo (at x=0)

334

inside the annular space of the reactor was evaluated and the results are shown in Figure

335

6. Raytracing results were in agreement with the predictions of the modified ESVE

336

models, LSDE, and ESDE, which all assumed diffuse emission from the lamp. The

337

fluence rate predicted by raytracing was approximately 5% higher than the other models

338

for some locations near the central region of the annular space. This may have been

339

partly because of differences in the model geometry itself, since in the raytracing

340

approach the thickness of the lamp, quartz, and reactor tubes were included in the

341

simulation, as was the reflective steel lamp support structure.

342

differences will contribute to variations in the fluence rate predictions. Another factor

343

that could affect the actual fluence rate is absorption/re-emission of radiation within the

344

lamp plasma, which was not accounted for in the raytracing simulations.


These geometric

In the


345

raytracing calculations, the inner cavity of the lamp arc was assigned a material property

346

of zero absorption.

347

measurements and the ESVERA results (with at most 5% relative difference), which is

348

considered the most inclusive and accurate model among the FV numerical models.12

Generally, raytracing predictions agreed with the experimental

349 350

Figure 5. Fluence rate (irradiance) as a function of axial position measured along

351

the reactor outer wall (2.5 cm away from the lamp axis) of the annular photo-reactor.

352

Raytracing (red curve) vs. experimental measurements and other numerical models.12

353

Adapted from reference [12].


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Page 19 of 29


354 355

Figure 6. Radial fluence rate profiles within the annular region of the UV reactor (at the

356

vertical axis of the lamp), as simulated by various models,12 including raytracing.

357

Adapted from reference [12].

358 359

Glass reactor. Estimated values of fluence rate for this reactor based on raytracing

360

were 5-9.5% and 10-40% higher for air and water, respectively, than the corresponding

361

measurements by the MSFD. Figures 7a and 7b provide comparisons of raytracing

362

simulation results and MFSD measurements for the reactor filled with air and water,

363

respectively. One reason for the discrepancy between simulated and measured values

364

was that the raytracing results were based on a spherical receptor, whereas the MSFD

365

involves a cylindrical detector. This was assessed by re-calculating fluence rate by

366

raytracing using cylindrical receptors of the same size as the MSFD detector (0.3 x 1

367

mm) and comparing these results with the predictions of fluence rate using spherical

368

receptors based on the theoretical definition of fluence rate (Figure S9).


Spherical


369

receptors are able to receive radiation equally from all angles, hence it is expected that

370

the sphere can capture more rays than a cylinder that has a similar cross-sectional area.

371

The ratio of the Eo predicted using spherical receptors to the cylindrical receptors was

372

used as a shape factor to account for the difference between the raytracing results and the

373

experimental measurements. It should also be noted that the cylindrical receptors were

374

located parallel to the lamp, similar to the detector orientation during the experiments.

375

Qiang et al.23 showed that the vertical angular response of the MFSD deviated somewhat

376

from the ideal cosine angular response and this was corrected by applying an angular

377

response correction factor of 1.08 to the MFSD readings. This factor was determined

378

from the average fluence rate ratio of the parallel to perpendicular detector orientations

379

with respect to the lamp axis.


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Page 21 of 29


250

(a)

Ray Tracing MFSD

2


200

150

100

50

0 0

5

10

15

20

25

30

35

Radial Distance from Sleeve (mm)

380 200

(b) Ray Tracing UVT = 95% MFSD UVT = 95% Ray Tracing UVT = 85% MFSD UVT = 85%

2


160

120

80

40

0 0

5

10

15

20

25

30

35


381 382

Figure 7. Radial distribution of fluence rate: (a) and (b) fluence rate in air and water

383

medium, respectively. Raytracing simulation results are compared with measurements in

384

both panels.



385

Figures 8 and 9 illustrate the results of raytracing simulations as radial and axial

386

distributions of fluence rate, respectively for the glass reactor, after being modified by

387

receptor shape and angular response factors against UVCalc3D results and experimental

388

measurements. After considering the factors described above, it appears that raytracing

389

can provide accurate estimates of fluence rate spatial distribution, as measured by the

390

MFSD. Raytracing estimates were within 0.7-14% of the measured values for air and 0.6

391

to 13% for water, except around the vertical end regions of the lamp. Neither of the

392

corrections explained the deviations of fluence rate values at an axial distance of 12 cm

393

or more from the lamp length center which reached up to 400% over prediction,

394

especially at the closest radial location to the lamp (3 mm radial distance) as seen in

395

Figure 9. This is discussed in more detail in the SI (section 7).


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Page 23 of 29


250

(a) Air

Measurements Raytracing with correction

2


200

150

100

50

0 0

5

10

15

20

25

30

35


250

(b) Water

Measurements T=95% Measurements T=85% Raytracing with Correction, T=95% Raytracing with Correction, T=85%

2


200

150

100

50

0 0

396

5

10

15

20

25

30

35


397

Figure 8. Radial distribution of fluence rate: (a) and (b) fluence rate in air and water,

398

respectively, for the glass reactor based on raytracing with MFSD shape and angular

399

response correction factors included.



(a) Air

250 2


Page 24 of 29

200 150 100 50 0 0

20

40

60

80

100

120

140

160

Axial Distance from Lamp Center (mm)

(b) Water, UVT = 95%

2


250 200 150 100 50 0 0

20

40

60

80

100

120

140

160

140

160

MFSD 3 mm UVCalc 3 mm Ray Tracing 3 mm MFSD 8 mm UVCalc 8 mm Ray Tracing 8 mm MFSD 13 mm UVCalc 13 mm RayTracing 13 mm MFSD 28 mm UVCalc 28 mm Ray Tracing 28 mm


(c) Water, UVT = 85%

2


250 200 150 100 50 0 0

20

40

60

80

100

120


400 401

Figure 9. Comparison of fluence rate field axial distributions for glass reactor in (a) air,

402

(b) water (UVT 95%), and (c) water (UVT 85%). MFSD measurements as well as

403

UVCalc (solid curves) and raytracing (dashed curves, adjusted by shape and angular

404

response corrections) predictions are included.


Page 25 of 29


405

The results of this study illustrate the ability of raytracing models to simulate the

406

spatial distribution of UV fluence rate in simple photochemical reactors. Raytracing

407

simulations provided predictions of fluence rate in basic reactor configurations with

408

single LP Hg UV lamps that agreed with chemical actinometer measurements and the

409

micro-fluorescent silica detector. The numerical (graphical) description of source and

410

reactor geometry, along with the ability to assign measurable optical properties to

411

materials that comprise the simulation domain allow for accurate simulations of fluence

412

rate distributions within UV systems. Specific reactor components that were accounted

413

for in these simulations included the UV lamp, quartz sleeve, reactor geometry/walls, and

414

fluid media. As such, raytracing tools may be applied as an alternative to other UV

415

irradiance numerical models, including LSI, MSSS, UVCalc, ESVE, and DO.

416

UV lamps were represented in these simulations as perfect arc cylinders enclosed in

417

a cylindrical quartz envelope. UV radiation was allowed to emanate uniformly over the

418

surface of the internal lamp arc. Future applications of raytracing may account for

419

variations in the radiation output, based on physical measurements of lamp output. These

420

models could be modified to account for non-uniformity in lamp output due to the effects

421

of lamp aging and fouling.

422

All models presented herein addressed simple single-lamp reactors; however,

423

multiple-lamp UV systems can easily be incorporated since the fluence rate is spatially

424

additive.

425

■ ASSOCIATED CONTENT

426

Supporting Information. Additional text, three tables, and twelve figures, describing

427

schematic illustration of basic photoreactor, emission pattern and modeling approaches of



428

UV radiation, variation in fluence rate predictions according to the size of the spherical

429

receptors and the initial source of rays used, schematic illustrations of the simulated

430

photoreactors with single UV lamp, comparison between fully transparent spherical

431

receptors and cylindrical receptors, radiant intensity distribution plots, and lastly

432

comparison of fluence rate predictions from fully transparent spheres versus fully

433

absorbent spheres. This material is available free of charge via the Internet at

434

http://pubs.acs.org.

435

■ AUTHOR INFORMATION

436

Corresponding Author

437

*

438

Notes

439

The authors declare no competing financial interest.

440

■ ACKNOWLEDGEMENTS

Phone: 1-765-494-0316; e-mail: [email protected].

441

The authors gratefully acknowledge financial support from the Citizen’s Energy, the

442

Water Environment Research Foundation (WERF), and the Edward M. Curtis Visiting

443

Professorship in the Lyles School of Civil Engineering at Purdue University.

444

■ REFERENCES

445 446 447 448

(1) Wastewater Technology Fact Sheet Ultraviolet Disinfection; US Environmental Protection Agency: Washington, DC, 1999. (2) Meierhofer, R.; Wegelin, M., Solar Water Disinfection - A guide for the application of SODIS. 2002.


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(3) Mbonimpa, E. G.; Vadheim, B.; Blatchley III, E. R., Continuous-flow solar UVB disinfection reactor for drinking water. Water Res. 2012, 46 (7), 2344-2354. (4) IUPAC, Compendium of Chemical Terminology Gold Book. International Union of Pure and Applied Chemistry: 2014; Vol. 2.3.3.

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(5) Ultraviolet Disinfection Guidance Manual for The Final Long Term 2 Enhanced

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Surface Water Treatment Rule; US Environmental Protection Agency: Washington, DC,

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2006.

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(6) Chiu, K.; Lyn, D. A.; Savoye, P.; Blatchley III, E. R., Integrated UV Disinfection Model Based on Particle Tracking. J. Environ. Eng. 1999, 125 (1), 7-16. (7) Jacob, S. M.; Dranoff, J. S., Light Intensity Profiles in a Perfectly Mixed Photoreactor. AlChE J. 1970, 16(3), 359-363.

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(8) Blatchley III, E. R., Numerical Modelling of UV Intensity: Application to

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Collimated-Beam Reactors and Continuous-Flow Systems. Water Res. 1997, 31 (9),

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2205-2218.

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(9) Bolton, J. R., Calculation of Ultraviolet Fluence Rate Distributions in an Annular

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Reactor: Significance of Refraction and Reflection. Water Res. 2000, 34 (13), 3315-3324.

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(10) Liu, D.; Ducoste, J. J.; Jin, S. S.; Linden, K., Evaluation of alternative fluence

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rate distribution models. J. Water Supply Res. T. 2004, 53 (6), 391-408.

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(11) Irazoqui, H. A.; Creda, J.; Cassano, A. E., Radiation Profiles in an Empty

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Annular Photoreactor with a Source of Finite Spatial Dimensions. AlChE J. 1973, 19(3),

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(12) Duran, J. E.; Taghipour, F.; Mohseni, M., Irradiance modeling in annular

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photoreactors using finite-volume method. J. Photochem. Photobiol., A: Chemistry 2010,

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215 (1), 81-89.

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(13) Kowalski, W. J.; Bahnfleth, W. P.; Witham, D. L.; Severin, B. F.; Whittam, T. S.,

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Mathematical Modeling of Ultraviolet Germicidal Irradiation for Air Disinfection.

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Quantitative Microbiology 2000, 2 (3), 249-270.

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(14) Lau, J.; Bahnfleth, W.; Mistrick, R.; Kompare, D., Ultraviolet Irradiance

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Measurement and Modeling for Evaluating The Effectiveness of In-Duct Ultraviolet

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Germicidal Irradiation Devices. HVAC&R Research 2012, 18 (4), 626-642.

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(15) Kuhn, H. J.; Beaslavsky, S. E.; Schmidt, R., Chemical Actinometry. IUPAC 2004, 76 (12), 2105-2146. (16) Rahn, R. O., Potassium Iodide as a Chemical Actinometer for 254 nm Radiation: Use of lodate as an Electron Scavenger. Photochem. Photobiol. 1997, 66 (4), 450-455.

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(17) Rahn, R. O.; Stefan, M. I.; Bolton, J. R., The Iodide/Iodate Actinometer in UV

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(18) Li, M. K.; Qiang, Z. M.; Li, T. G.; Bolton, J. R.; Liu, C. L., In situ measurement

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Ray Tracing for Fluence Rate Simulations in Ultraviolet Photoreactors

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