Modeling of Formaldehyde Photocatalytic Degradation in a

Article pubs.acs.org/IECR

Modeling of Formaldehyde Photocatalytic Degradation in a Honeycomb Monolith Reactor Using Computational Fluid Dynamics Xin Wang,† Xin Tan,‡ and Tao Yu*,†,§ †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China School of Science, Tibet University, Lhasa City 850000, China § TU-NIMS Joint Research Center, Tianjin University, Tianjin 300072, P. R. China ‡

ABSTRACT: In this article, simulations were conducted on a pilot-scale honeycomb monolith reactor for the photodegradation of formaldehyde. The monoliths in the reactor were treated as porous media, and the local light intensity across the porous media was modeled by the discrete ordinates model with one adjustable parameter, namely, the absorption coefficient of the monolith channel wall. This absorption coefficient was estimated by a trial-and-error method based on the observed modeling results of light intensity in a single channel. Then, the formaldehyde degradation in a monolith reactor was simulated by the proposed model. The proposed model achieved a reasonable agreement between the simulation results and the published experimental data. Based on the modeling approach provided in this article, the effect of humidity on the photodegradation of formaldehyde was investigated. The data indicate that the reaction is first-order in the reactants for the intended applications such as purification of air in office buildings and commercial aircraft. The optimal design of the monolith reactor was also investigated. The effects of a dimensionless geometric parameter and the number of lamps were investigated and correlated in terms of the formaldehyde conversion yield. Moreover, the optimal monolith-to-lamp-distance ratio, β, was correlated as β = 1.622n + 0.1038, where n is the number of lamps.

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reactors,15 coated honeycomb monolith reactors,16,17 fluidizedbed reactors,18 optical-fiber photoreactors,19−22 and photoCREC-air reactors.23 These reactors have been modeled using various approaches such as computational fluid dynamics (CFD) and Monte Carlo simulations. Recently, the CFD modeling approach was successfully used as a tool to investigate photoreactors. Mohseni and Taghipour24 employed both CFD modeling and experimental approaches to study vinyl chloride removal in an annular photocatalytic reactor and reported good agreement of the model with the experimental data. SalvadoEstivill et al.25 combined CFD modeling with radiation field modeling and photocatalytic reaction kinetics to model trichloroethylene oxidation in a flat-plate reactor. Hossain et al.26 presented a three-dimensional convection−diffusion− reaction model to simulate formaldehyde oxidation in a monolith photocatalytic reactor. Queffeulou et al.27 modeled the fluid dynamics and photocatalytic reaction with a CFD approach using kinetic parameters previously determined in a batch reactor, and the model prediction and experimental results were found to be in good agreement. It is well-known that the honeycomb monolith reactor has some inherent attractive characteristics such as low pressure drop and high catalyst surface area.28 Furthermore, monolith supports are commercially available. Monoliths are widely used in automobile exhaust emissions controls and in NOx reduction in power-plant flue gases by selective catalytic reduction (SCR). Recently, monoliths were employed in heterogeneous photo-

INTRODUCTION Indoor air quality (IAQ) in office buildings,1 vehicles,2 and commercial aircraft3 has received increasing attention from the scientific community in the past two decades. This is due to its impact on human health and comfort. Efforts to save energy might lead to inadequate heating−ventilation−air-conditioning (HVAC) systems in buildings, allowing an accumulation of indoor contaminants in enclosed spaces. This poor air quality can cause adverse health effects such as irritation, headache, dizziness, dry cough, and fatigue.4,5 This phenomenon is known as “sick building syndrome” (SBS). This syndrome is usually associated with the presence of volatile organic compounds (VOCs).6,7 VOCs represent a major group of indoor contaminants with hundreds of different species. Among these VOCs, formaldehyde (HCHO) is one of the most typical8 and is of particular interest because of its abundance in indoor air environments.9,10 Formaldehyde, the simplest aliphatic aldehyde, is a strong-smelling colorless gas. Materials used in furniture, paints, and textiles contain formaldehyde. Indoor concentrations of HCHO can reach up to 2 ppm if the environment is not well-ventilated, but are typically below 0.1 ppm.7 In this range, gaseous HCHO can cause unhealthy impacts on humans. To prevent the syndrome and improve indoor air quality, the efficient removal of VOCs in these enclosures has become a crucial issue. Photocatalysis has already been demonstrated to be an effective technology for the elimination of various gaseous pollutants.11,12 The advantages of this technology include the following: It can occur at room temperature and pressure and is able to oxidize many gaseous contaminants to benign products.13 Many photocatalytic reactor configurations have been investigated, such as annular packed beds,14 flat plate © 2014 American Chemical Society

Received: Revised: Accepted: Published: 18402

April 22, 2014 September 3, 2014 November 10, 2014 November 10, 2014 dx.doi.org/10.1021/ie5016427 | Ind. Eng. Chem. Res. 2014, 53, 18402−18410

Industrial & Engineering Chemistry Research

Article

In a typical experiment, the entrance and exit light intensities of a particular channel were measured with a UV radiometer. The entrance light intensity was approximately 12 mW·cm−2. Because of the detection limitation of the photometer, we could not obtain reliable values for a single-channel measurement for channel lengths greater than 2.54 cm. Therefore, the exit light intensities of four adjacent monolith channels were measured. Then, the measured value was divided by 4 to obtain an average single-channel value. Values directly measured for a single channel were in good agreement with those determined by this method.

catalytic treatment of air and might prove to be a suitable candidate for indoor air purification. Thus, the honeycomb monolith reactor was investigated in this work. The common type of this kind of reactor is composed of many modules such as that represented in Figure 1. The lamps irradiate the

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CFD MODELING The honeycomb monoliths in the photoreactor were simulated as porous zones using Fluent. The following general assumptions were made: (1) The system was operated under isothermal conditions. (2) The flow was laminar and incompressible. (3) Gas-phase absorption, scattering, and emission of radiation were negligible.26 (4) The film coated on the monolith walls was uniform and sufficiently thick that no light could transmit through the film.26 The governing equations for modeling the system are as follows: The mass conservation is described by the partial differential equation

Figure 1. Full-scale photocatalytic honeycomb monolith reactor.

monolith front and back faces, and air flowing in the duct is forced through the monolith channels, which are coated with the active titania photocatalyst. Most previous studies of honeycomb reactor modeling considered only thermal catalytic reactions in which lamp radiation was not involved.29 This work focuses on the photocatalytic degradation of formaldehyde in a monolith reactor using a CFD modeling approach. The main objective of the present work was to provide a modeling approach that can be used to investigate the reactor performance under different operating conditions (such as humidity levels in the intended HVAC applications) and optimize the reactor design. To the best of our knowledge, very few reports have been published so far about the optimization of monolith reactors. In this article, first, the light distribution in a single channel of a monolith was modeled by the Monte Carlo method,30 and the absorption coefficient of the channel wall was estimated based on the modeling results. Second, a CFD simulation was conducted on a pilot-scale honeycomb monolith reactor for the photodegradation of formaldehyde. The simulation and experimental results were compared in terms of conversion yield to validate the methodology. Third, based on the modeling approach used in this work, the effects of water vapor levels on the reactor performance for intended applications (such as air purification in office buildings and commercial aircraft) were investigated. Finally, optimization of this monolith photocatalytic reactor configuration was conducted.

∂(γρ) + ∇·(γρv ⃗) = 0 ∂t

(1)

where ρ is the density; v ⃗ is the velocity vector of the fluid; γ is the porosity of the monolith, which was taken as 0.5;16 and t is the time. The conservation of momentum in the monolith reactor is given by ∂ (γρv ⃗) + ∇·(γρvv⃗ ⃗) = −γ ∇p + ∇·(γτ ) + γρg + Sφ ∂t (2)

where p is the pressure, τ is the viscous stress tensor, and g is the gravitational force. Sϕ represents the momentum sink term, which includes the pressure drop due to the monolith channels and the catalyst support. In this work, the monoliths are modeled by using porous media formulations instead of introducing computational grids, which are in the range of submicron compared with the overall monolith reactor.29 Sϕ is composed of two parts: a viscous loss term (Darcy, the first term on the right-hand side of eq 3) and an inertial loss term (the second term on the right-hand side of eq 3)

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EXPERIMENTAL SECTION A series of circular-channeled ceramic cordierite honeycomb monoliths with a nominal cell density of 50 cells per square inch (CPSI) and lengths varying from 0.635 to 5.08 cm were used. The actual channel width was 0.295 cm for the 50 CPSI monoliths. To approximate a diffuse light source, a parallel bank of four 8-W fluorescent black light lamps (365 ± 30 nm) with aluminum reflectors was assembled. These lamps were positioned in front of the each monolith channel mouth such that the distance from the bank to the center monolith channels was 5.08 cm. The light intensities at the channel entrance and exit were measured with a UV radiometer (Photoelectric Instrument Factory of Beijing Normal University, model UVA). The UV radiometer was equipped with a 365-nm sensor and was capable of detecting light with wavelengths between 320 and 400 nm. A solid black shield was employed to allow light only into the channels of interest.

⎛μ ⎞ C Sφ = −⎜ v ⃗ + 2 ρ|v ⃗|v ⃗⎟ ⎝K ⎠ 2

(3)

where K is the permeability and C2 is the inertial resistance factor. The monoliths can be characterized as a packed bed, and the Ergun equation was used to derive porous media inputs for a packed bed Dp2

K=

γ3 150 (1 − γ )2

(4)

C2 =

3.5 (1 − γ ) Dp γ3

(5)

where Dp is the particle diameter. For a packed bed, the specific surface area of the particles in the packed bed αV can be 18403

dx.doi.org/10.1021/ie5016427 | Ind. Eng. Chem. Res. 2014, 53, 18402−18410


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expressed in terms of the porosity γ and the area of the particle outer surface Sp αV =

(1 − γ )Sp Vp

=

6(1 − γ ) 6(1 − γ ) πDp2 = 3 Dp πDp

through multiplication by the illuminated specific area of the photocatalyst (αs) ⎛ I ⎞0.5 K 4C W K1C F − R i = K 0⎜ ⎟ αs ⎝ IG ⎠ 1 + K1C F + K 2C W 1 + K3C F + K4C W

(6)

(11)

where Vp is the volume of the particle. Therefore, the Dp can be expressed in terms of αV as Dp =

6(1 − γ ) αV

Equation 11 was then introduced into the CFD solver as a userdefined function (UDF). The light intensity distribution in the monolith reactor can be described by the following general radiative transfer equation (RTE)

(7)

The species transport equation takes the form ∂ (γρYi ) + ∇·(γρvY ⃗ i ) = −∇·Ji ⃗ + R i ∂t

dIλ( r ⃗ , s ⃗) + κλIλ( r ⃗ , s ⃗) + σsIλ( r ⃗ , s ⃗) ds ⃗ 4π σ Iλ( r ⃗ , s ⃗′) φ( s ⃗ , s ⃗′) dΩ′ = s 4π 0

(8)

∫

where Ri is the net rate of production or depletion of compound i by chemical reaction and Ji⃗ is the diffusion flux of species i and is given by Ji ⃗ = −ρDi ,m∇Yi

where Iλ(r,⃗ s)⃗ is a beam of radiation intensity in the medium, which depends on position r ⃗ and direction s;⃗ κλ and σs are the absorption and scattering coefficients, respectively, of the medium; and ϕ(s,⃗ s′⃗ ) is a phase function that indicates the inscattering of incident radiation. In this article, the RTEs were solved using the discrete ordinate (DO) model. The DO radiation model solves an RTE for a finite number of discrete solid angles, each associated with a vector direction s ⃗ fixed in the global Cartesian system (x, y, z). The DO radiation model does not perform ray tracing. Instead, the RTE is transformed into as many transport equations as there are solid angles with direction s.⃗ The solution method is the same as that used for the momentum and energy equations. The angular discretization of the solid angles is defined by the user. Each quadrant of the Cartesian coordinate system is discretized into Nθ × NΦ solid angles, so in three-dimensional modeling, a total of 8 × Nθ × NΦ equations are solved for each wavelength band. An angular discretization of 6 × 6 was used in this study, and the number of pixels (Nθp × NΦp) was set to be 3 × 3 (the pixilation discretizes the overhanging control angle of the control volume faces that do not align with global angular discretization). The incident radiation at any point from all the directions is given by

(9)

where Di,m is the diffusion coefficient of species i, for which a constant value of 2.88 × 10−5 m2·s−1 was used in the simulation. A bimolecular form of the Langmuir−Hinshelwood (L−H) kinetic model was used to simulate the photocatalytic reaction in the monoliths. This model was highly successful in correcting the photocatalytic reaction rate for formaldehyde with a ceramic foam reactor in a previous study.31 A simplifying assumption was made, namely, that the reaction products, carbon dioxide and carbon monoxide, did not influence the observed oxidation rates and that only the formaldehyde and water vapor were important. The influence of any reaction intermediates was also neglected. With these assumptions, the L−H rate equation is ⎛ I ⎞0.5 K 4C W K1C F −ri = K 0⎜ ⎟ ⎝ IG ⎠ 1 + K1C F + K 2C W 1 + K3C F + K4C W (10)

where K0 is the rate constant, which is a function of temperature and catalyst properties; I is the local incident radiation intensity in the monolith; IG is the radiation intensity for which the kinetic constants were evaluated;31,26 K1, K2, K3, and K4 are the Langmuir adsorption equilibrium constants; and CF and CW are the gaseous concentrations of the formaldehyde and water vapor, respectively. The corresponding values of reaction constants are listed in Table 1. The two ratios in eq 10 represent competitive adsorption between formaldehyde and water vapor for the same adsorption site. To enable the expression of Ri in eq 8 on a volumetric basis, eq 10 was then converted to the volumetric reaction rate

Iλ( r ⃗) =

parameter

value formaldehyde 1.05 1.02 0.00020 1.11 0.015

∫0

4π

Iλ( r ⃗ , s ⃗) ds

(13)

In this application, because there was no absorption or scattering by the gas medium outside the monolith channels, both the absorption and scattering coefficients were set to zero, so that eq 12 reduces to

dIλ( r ⃗ , s ⃗) =0 ds ⃗

(14)

However, there was great loss of light in the monolith channel due to absorption by the channel wall. Therefore, by introducing the absorption coefficient κλ of the channel wall and assuming that the scattering could be neglected compared to the absorption, we reduced eq 12 to

Table 1. Kinetic Parameters of the Langmuir−Hinshelwood Model31

gas K0(μmol·cm−2·h−1) K1 (ppm−1) K2 (ppm−1) K3 (ppm−1) K4 (ppm−1)

(12)

dIλ( r ⃗ , s ⃗) + κλIλ( r ⃗ , s ⃗) = 0 ds ⃗

(15)

The absorption coefficient of the channel wall, κλ in eq 15, was estimated by a trial-and-error method based on the separate Monte Carlo30 simulations of the light intensity profile in a single monolith channel. 18404



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The methodology employed for this simulation is schematically summarized in Figure 2. The three-dimensional physical

Figure 3. Comparison of predicted cross-sectional intensities at the monolith outlet with experimental data. Figure 2. Modeling methodology.

method was deemed acceptable and was used to predict the UV flux profile in a single monolith channel in further simulations. Figure 4 shows the predicted dimensionless UV flux across a single-faced irradiated monolith as a function of the

domain of the photoreactor is shown in Figure 1. In this study, the pilot-scale reactor was 2.0 m long and could accommodate up to six lamp banks (each consisting of four UV lamps) and five square honeycomb monoliths (see Figure 1). The two lamp banks were located 2.5 cm from the monolith. A monolith with a depth of 2.54 cm having a surface area of 30.48 cm × 30.48 cm was used in the modeling. Physical and chemical properties of species (i.e., formaldehyde, water vapor, and air as the carrying medium) were specified for calculating the coefficients of the governing equations described above. The boundary conditions used in this study were as follows: (1) The inlet velocity32 with formaldehyde and water vapor mass fractions and the pressure outlet with a gauge pressure of 0 were specified as boundary conditions for the inlet and outlet flows, respectively. (2) The monoliths were modeled using porous media formulations. (3) A diffuse semitransparent wall was assumed for the UV lamp surface. (4) A diffusely reflecting aluminum wall was assumed for the reactor wall. A segregated, pressure-based solver was used to perform the numerical experiments. The convergence criterion of 10−5 was specified for each scaled residual component of mass, velocity, species, and intensity.

Figure 4. Dimensionless UV flux vs dimensionless axial distance for a monolith irradiated from one side.

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RESULTS AND DISCUSSION Light Intensity Distribution in a Single Monolith Channel. To obtain the value of the absorption coefficient of the channel wall κλ, the UV flux profile in a single channel was obtained first using a Monte Carlo method,30 and the simulation results are directly given in Figure 3. Furthermore, Figure 3 also compares the experimental results of dimensionless cross-sectional exit UV intensities for the uncoated monoliths with the simulation results as a function of the channel aspect ratio (AR). The channel aspect ratio (AR) is a dimensionless term and is defined as the channel length divided by the width of a single monolith channel. The reflectivity of the monolith channel wall was taken to be 0.5. From the comparison results in this figure, one can see some deviations in the predicted UV flux profile compared to the experimentally measured results. Such deviations can be attributed to the uncertainty of the experimental measurements and the wall reflectivity value. However, the differences are within the limits of confidence reported in Alexiadis;30 thus, the Monte Carlo

dimensionless axial distance (X). The dashed line represents the Monte Carlo simulation results of the UV flux profile. As can be seen in this figure, the UV flux is the highest at the monolith inlet because the irradiation is coming from the channel mouth (X = 0). The UV intensity drops sharply with increasing axial distance. The UV flux intensity rapidly decreases to 30% of the incoming flux at an axial distance of X = 1 and to 1% of the incoming flux at an axial distance of X = 3. Beyond an axial distance of X = 3, the photocatalyst is nearly subjected to operation under “dark” conditions. This means that the photocatalyst coated on the dark portion (X > 3) of the monolith cannot be sufficiently illuminated, and further studies16,30 demonstrated that the photon absorption flux decays sharply to less than 1% when the monolith axial distance is higher than approximately 3. This conclusion suggests that a shorter axial distance of monoliths is preferred for photocatalytic decomposition applications. From the above simulation results, by a trial-and-error method, the optimum fit 18405



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Simulation of Formaldehyde Photodegradation in a Monolith Photoreactor and Model Validation. To validate the CFD simulation results, the simulations were conducted under the same experimental conditions as used by Hossain et al.26 Table 2 reports the experimental details and modeling results under different conditions. Take case 13 as an example: The concentration of formaldehyde in the inlet air was 0.3 ppm, with 2800 ppm water vapor at a flow rate of 19.35 × 10−2 m3·s−1 to the monolith, reactor which contained five doublefaced irradiated monoliths and six lamp banks. The experimentally measured conversion of formaldehyde was 60%, whereas the predicted conversion was 64.5%, with an error of −7.5%. Figure 6 illustrates the quality of the model predictions compared with the experimental results for formaldehyde

closely matching the Monte Carlo simulation results occurred at a value of κλ = 200 m−1; the corresponding DO fitting curve of the UV flux profile is shown by the solid line in Figure 4. There are some deviations in the DO-predicted UV flux profile compared to the Monte Carlo simulation profile (the greatest differences occur at the dimensionless axial distance of 3). However, the overall DO simulation fitting results match the Monte Carlo simulation results very well. As shown in Figure 5, for a double-faced irradiated monolith, the Monte Carlo modeling profile of UV flux (dashed line) is

Figure 5. Dimensionless UV flux vs dimensionless axial distance for a monolith irradiated equally from both sides.

distributed in a parabolic manner. Under these irradiation conditions, the UV flux intensity reaches a minimum value at the center of the monolith channel. Lamps located on both sides of the monolith reduce the dark zones, thereby improving the distribution of light intensity on the surface of the monolith. In this case, the light intensity at the middle of the channel is about 3% of the value at the channel mouth. The DO fitting curve of the UV flux profile is shown by the solid line in Figure 5, and the comparison between these two curves further demonstrates that the estimated value could be used to simulate the local UV flux in the monoliths of the pilot-scale photoreactor.

Figure 6. Experimental conversion vs predicted conversion for formaldehyde degradation.

degradation. For an ideal match, all of the data points should fall on the diagonal of the plot. As can be seen in Figure 6, the model-predicted results generally agree well with those obtained in the experiments, although some mismatch between the modeling and experimental data also exists. Some possible reasons for the mismatch can be attributed to the temperature

Table 2. Comparison of Model and Experiment for Formaldehyde26 conversion (%) case

flow rate (×10−2 m3·s−1)

UV flux (W·m−2)

inlet conc (ppm)

water conc (ppm)

lamp/ surface

monolith length (cm)

measured

predicted

difference

1 2 3 4 5 6 7 8 9 10 11 12 13

9.44 9.44 19.35 2.60 2.60 2.60 2.60 2.60 2.60 2.60 2.60 9.44 19.35

65 65 65 65 65 65 65 65 65 65 65 65 65

0.4 0.4 0.3 1.9 1.9 2.1 2.1 2.1 2.1 2.1 2.1 0.7 0.3

3900 3900 2800 6000 6000 2700 2700 2700 2700 2700 2700 4800 2800

8/4 16/8 8/4 4/1 4/2 4/1 4/2 4/1 4/2 4/1 4/2 8/4 24/10

2.54 2.54 2.54 2.54 2.54 1.27 1.27 2.54 2.54 3.81 3.81 2.54 2.54

50 82 24 44 77 35 52.5 42.5 60.5 43.5 66 54 60

51.1 93.33 29.86 34.0 65.31 27.8 48.7 34.3 58.8 36.1 62.0 60.7 64.5

−2.2 −13.8 −24.4 22.7 15.2 20.6 7.2 19.3 2.8 17.0 6.1 −12.4 −7.5

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effect. For formaldehyde decomposition, a temperature rise of 20 °C can cause the oxidation rate to decrease by 10%.33 Nonetheless, the good agreement between the predicted and experimental results reveals that the novel modeling approach presented in this work can be used to predict the photocatalytic degradation of formaldehyde in a honeycomb monolith reactor. Effect of Humidity Level. In this study, the influence of the humidity level was examined with various concentrations of water vapor. Different water vapor levels were applied to a fixed concentration of formaldehyde. Figure 7 shows the predicted

Figure 8. Predicted formaldehyde conversion vs formaldehyde level for different humidity levels (inlet flow rate = 2.6 × 10−2 m3·s−1, UV flux = 65 W·m−2, lamp/surface = 4/2).

formaldehyde level increased. Formaldehyde levels found in aircraft are usually below 1 ppm, and the humidity levels in aircraft are also very low. Fortunately, the predicted conversions in Figure 8 under these formaldehyde and humidity levels are very high. Furthermore, as shown in Figure 9, the formaldehyde

Figure 7. Effect of humidity level on the formaldehyde conversion for different formaldehyde levels (inlet flow rate = 2.6 × 10−2 m3·s−1, UV flux = 65 W·m−2, lamp/surface = 4/2).

conversion of formaldehyde versus the initial water vapor concentration for values varying from 350 to 25000 ppm. The effect of the water vapor level on the formaldehyde conversion was found to be dependent on the concentration of formaldehyde, and the location of the maximum conversion values shifted to higher humidity as the formaldehyde concentration was increased. Along the 2.1 ppm formaldehyde data curve, the predicted conversion was enhanced by water vapor at concentrations up to 2700 ppm and then inhibited at concentrations above 2700 ppm. Under relatively low water vapor contents (below 2700 ppm), water molecules or hydroxyl groups behave as hole trappers, forming surface-adsorbed hydroxyl radicals. The hydroxyl radicals formed on illuminated TiO2 can not only directly attack formaldehyde molecules but also suppress electron−hole recombination. Therefore, the conversion of formaldehyde increased with increasing water vapor. However, when the concentration of water vapor was high (above 2700 ppm), the water molecules could compete with the formaldehyde molecules on the catalyst surface sites during adsorption. Thus, the conversion of formaldehyde decreased with increasing water vapor level. The relative humidity level range for HVAC applications at room temperature is roughly 40−60% (11000−16000 ppm), and for aircraft, it is about 15−30% (4000−8000 ppm). Formaldehyde levels found in problem buildings are about 0.5− 2 ppm. Thus, reactor performance under these formaldehyde and relative humidity levels was also investigated. Figure 8 shows the dependence of the predicted conversion on the formaldehyde level under different humidity levels. As can be seen in Figure 8, the predicted conversion decreased as the

Figure 9. Predicted formaldehyde degradation rate vs formaldehyde level for different humidity levels (inlet flow rate = 2.6 × 10−2 m3·s−1, UV flux = 65 W·m−2, lamp/surface = 4/2).

oxidation rate exhibits a nearly first-order dependence on formaldehyde level in the range from 0.05 to 2.1 ppm. As stated above, the reactor performance would show a first-order dependence on formaldehyde levels under these relative humidity levels for the intended HVAC applications. Effect of Reactor Geometric Parameters. In this work, the dependence of formaldehyde conversion on the reactor geometric parameters was also evaluated. Here, the reactor geometric parameters, n and β are defined as n = number of lamps β = H /D

where H is the height of the monolith and D is the distance between the lamp and the monolith. To best illustrate the 18407



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geometric details of the reactor, the corresponding geometric parameters are depicted in Figure 10.

Figure 10. Definition of the reactor geometric parameters.

Figure 12. Optimum value of β that maximizes conversion vs number of lamps n.

In the monolith photoreactor, a complex interaction exists among the fluid flow, light intensity distribution (number of lamps), and monolith-to-lamp spacing. To the best of our knowledge, no systematic study of monolith reactor optimization has accounted for all of these parameters simultaneously. Figure 11 shows the formaldehyde conversion for different values of β and n. Several general observations can be made.

In practice, when the number of lamps is greater than 5, the optimal design could become impractical in small monolith reactors, as the lamps should be placed close to the monolith (β > 8). Moreover, the fluid flow distribution over the monolith in small reactors might be obstructed by the relatively large physical dimensions of the lamps. Thus, fluid dynamic studies would be necessary when designing a monolith photocatalytic reactor.

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CONCLUSIONS In the present work, a systematic study of formaldehyde degradation in a honeycomb monolith reactor using CFD approach was performed, and the following conclusions were drawn: The CFD modeling approach presented in this article treated the monoliths in the reactor as porous media and was coupled with a simplified RTE to describe the local UV flux by introducing the absorption coefficient of the channel wall. In addition, the absorption coefficient of the channel wall was estimated by a trial-and-error method based on Monte Carlo simulation results. This absorption coefficient was then used in the subsequent simulation of a pilot-scale reactor. The simulation results matched the published experimental results well, thus validating the reliability of this modeling approach. Based on the modeling approach, the effect of humidity on formaldehyde photodegradation was investigated. Concentration levels ranging from sub-part-per-million to several parts per million as found in buildings, vehicles, and aircraft (the intended HVAC applications) were included in this evaluation. The effect of humidity on the formaldehyde conversion was found to depend critically on the concentration, and the reactor performance showed a first-order dependence on the formaldehyde level under these relative humidity levels for the intended applications. The effects of the monolith-to-lamp spacing and the number of lamps were investigated and correlated in terms of conversion yield. When the number of lamps was increased, it was found that the spacing between the monolith and lamp should be decreased to achieve an optimal configuration. The choice of an optimal number of lamps depends on further considerations of fluid flow dynamics over the monolith, especially in small reactors.

Figure 11. Predicted conversion vs β for different numbers of lamps (inlet flow rate = 2.6 × 10−2 m3·s−1, formaldehyde content = 2.1 ppm, water content = 2700 ppm, lamp/surface = 4/2).

First, as n increases, higher values of conversion are observed. Second, the values of conversion reach a maximum at specific values of β for different numbers of lamps. This relationship can be clearly identified for the cases shown in Figure 11. From the above simulation results, the relationship between the optimum value of β and the number of lamp n can be derived. The correlated result is shown in Figure 12. It can be seen from Figure 12 that the lamps should be placed closer to the monolith as their number increases. Furthermore, the following correlation for β was identified for the optimal design of monolith photocatalytic reactors

β = 1.622n + 0.1038 18408



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AUTHOR INFORMATION

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Corresponding Author

*E-mail: [email protected]. Tel.: +86-22-23502142. Notes

Ω = solid angle (sr)

REFERENCES

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 21406164, 21466035), the National Key Basic Research and Development Program of China (973 Program, No. 2012CB720100), the Natural Science Foundation of Tianjin (No. 13JCQNJC05700), the Research Fund for the Doctoral Program of Higher Education of China (No. 20130032120019), and the National Key Basic Research and Development Program of China (973 Program, No. 2014CB239300).

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NOMENCLATURE C2 = inertial resistance factor (m−1) CF = formaldehyde concentration (ppm) CW = water vapor concentration (ppm) D = distance between the lamp and the monolith (m) Di,m = diffusion coefficient of species i in the mixture (m2· s−1) Dp = bed particle diameter (m) g = gravitational force (m·s−2) H = height of the monolith (m) I = radiation intensity (W·m−2) IG = radiation intensity for which the kinetic constants were evaluated (W·m−2) Iλ = spectral radiation intensity (W·m−2) Ji⃗ = mass diffusion flux of species i (kg·m−2·s−1) K = permeability (m2) K0 = rate constant (μmol·cm−2·h−1) K1, K2, K3, and K4 = Langmuir adsorption equilibrium constants (ppm−1) n = number of lamps p = pressure (Pa) r ⃗ = position vector ri = rate of production or depletion of species i by photocatalytic reaction (mol·m−2·s−1) Ri = net rate of production or depletion of species i by chemical reaction (mol·m−3·s−1) s ⃗ = direction vector Sp = area of the particle outer surface (m2) Sϕ = momentum sink term (N·m−3) t = time (s) v ⃗ = velocity vector of the fluid (m·s−1) Vp = volume of a particle (m3) Yi = mass fraction of species i

Greek Letters

αs = illuminated specific area of the photocatalyst (m−1) αV = specific surface area (m−1) β = reactor geometric parameters γ = porosity of the medium δs = scattering coefficient (m−1) κλ = spectral absorption coefficient (m−1) λ = wavelength (nm) μ = viscosity of fluid (Pa·s) ρ = density (kg·m−3) τ = viscous stress tensor (N·m−2) ϕ(s,⃗ s′⃗ ) = phase function 18409



Article

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Modeling of Formaldehyde Photocatalytic Degradation in a

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