for the motor integrity. Therefore, it is also intended to design motors with water cooled
bearings.
Note that in this design step the fouling and corrosion were not considered, however, due to its meaning should be contemplated before product execution.
8. Conclusions
With the support of the CFD technique it was possible to foresee the water flow behavior
inside the frame channel without visualizing directly the water flow. Through the use of the CFD it was also possible to double the water speed inside the frame channel, thus reducing
the pressure drop in 18 % when compared with the initial design.
Another advantages provided by CFD were the reduction obtained both in the development
time and in the number of prototypes. These advantages have been proven in this work: in
spite of the 22 frame configurations that have been initially proposed, after the simulation results were obtained only the three best prototypes have been actually manufactured.
The use of thermography techniques in the field of electric motors helps to improve not only the development of products, but also the quality control and the maintenance of operating
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machines in the field. In this case, specifically, it was possible to visualize the guides
configuration and the water flow inside the frame channel preventing the need to destroy it.
9. Acknowledgement
The authors would like to thank all Weg colleagues that directly or indirectly participated in this project.
10. References
Fox, R. W. & Mcdonald, A. T., Introdução à mecânica dos Fluidos, fifth edition, 2001.
Incropera, F. P. & Witt, D. P., Introduction to Heat transfer, second edition by John Wiley & Sons, 1985.
John H. Lienhard IV & V, A Heat Transfer Textbook, third edition, published by Phlogiston Press, 2004.
Jones, W. P. & Launder, B. E. (1972), The Prediction of Laminarization with a Two-Equation Model of Turbulence, International Journal of Heat and Mass Transfer, vol. 15, 1972, pp. 301-314.
Kreith, F., Princípio da transmissão de Calor, translation of the 3rd american edition, 1977.
Kreith, F., The CRC Handbook of Thermal Engineering, CRC Press LLC, 2000.
Launder, B. E. & Sharma, B. I. (1974), Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disc, Letters in Heat and Mass Transfer,
vol. 1, no. 2, pp. 131-138.
Launder, B. E. & Spalding, D. D., Mathematical Models of Turbulence, Academic Press, London, 1972.
Menter, F. R. (1993), Zonal Two Equation k-ω Turbulence Models for Aerodynamic Flows, AIAA Paper 93-2906.
Menter, F. R. (1994), Two-Equation Eddy-Viscosity Turbulence Models for Engineering
Applications, AIAA Journal, vol. 32, no 8. pp. 1598-1605.
Nailen, R. L., Understanding the TEWAC Motor, IEEE Transactions on Industry Applications, vol. IA-11, nº. 4, July / august, 1975.
Roberge, P. R., Handbook of Corrosion Engineering, McGraw-Hill, 2000.
Wilcox, D.C., Multiscale model for turbulent flows, In AIAA 24th Aerospace Sciences Meeting.
American Institute of Aeronautics and Astronautics, 1986.
8
Computational Fluid Dynamics (CFD)
Modeling of Photochemical Reactors
Masroor Mohajerani, Mehrab Mehrvar and Farhad Ein-Mozaffari
Department of Chemical Engineering, Ryerson University, Toronto, Ontario
Canada
1. Introduction
Advanced oxidation processes (AOPs) play an important role in the degradation or the
production of a wide range of organic materials. Many organic compounds such as
pharmaceuticals, dyes, herbicides, and pesticides have been subjected to degradation and
remediation purposes in water and wastewater treatment systems using AOPs. Some of the
organic compounds such as drugs, vitamins, or fragrances could be also produced by
oxidation processes.
As the standard of living increases, many chemicals such as pharmaceuticals, pesticides,
herbicides, and dyes are extensively consumed. Each of these products may cause health
issues by their accumulation in aquatic environment. Pharmaceuticals such as antibiotics are partially metabolized and excreted by humans and animals. Improper disposal, dumping,
and accidental discharge of drugs lead to the increase of the concentration of compounds
such as analgesics, antibiotics, steroids, and hormones in aquatic environment, which cause
environmental and health problems. Residual pesticides and herbicides originate from the
direct pollutant in production plant, disposal of empty containers, equipment washing, and
surface runoff. High levels of these compounds are toxic, mutagenic, carcinogenic, and
tumorigenic. Some other wastes such as landfill leachate are subjected to advanced
treatment methods. Old landfill leachates (>10 years) are nonbiodegradable in nature due to the existence of organic compounds with high molecular weights. Although the composition
of landfill leachates varies widely with respect to the age of the landfill, type of wastes, and climate conditions, they can be categorized into four groups of dissolved organic matter,
inorganic macro components, heavy materials, and xenobiotic organic substances. Another
type of toxic chemicals which cannot be removed using conventional treatment methods is
endocrine disrupting compounds (EDCs). EDCs, especially the steroidal hormones, are well
recognized exogenous agents that interfere with the synthesis, action, and/or elimination of natural hormones in the body. Conventional processes are not effective in destruction of
these types of organic compounds; therefore, powerful advanced treatment processes are
required in order to mineralize them. There are several options for choosing an oxidation
process: wet air oxidation, supercritical water oxidation, incineration, and AOPs.
AOPs have been promising in the treatment of contaminated soils and waters. The AOPs
could be employed to fully or partially oxidize organic pollutants usually using a
combination of different oxidants. In contrary to the conventional physical and chemical
treatment processes, AOPs do not transfer pollutants from one phase to another, i.e., organic 156
Applied Computational Fluid Dynamics
pollutants are completely destroyed. Most AOPs are able to generate hydroxyl radicals.
These hydroxyl radicals are active and powerful, capable of reacting with almost all types of organics, including non-biodegradable and recalcitrant compounds. These oxidizing
hydroxyl radicals are initiated by photolysis, photocatalysis, sonolysis, radiolysis, and other AOPs alone or in combination in the presence of some reagents such as hydrogen peroxide
(H2O2), ozone, and homogeneous or heterogeneous catalysts. Hydroxyl radicals are
extremely powerful, short-lived oxidizing agent, and non-selective in nature and could react with a wide range of organic chemicals with reaction constant of several orders of
magnitude higher than the reaction with molecular ozone under the same conditions. AOPs
are used to convert toxic, non-biodegradable, inhibitory, and recalcitrant pollutants into
simpler and less harmful intermediates, so they could be treated subsequently in biological
processes. Due to the high operating and capital costs of AOPs, the complete mineralization
of organic compounds using AOPs is practically impossible; therefore they are mainly
combined with other processes such as biological systems to be cost-effective. With
sufficient contact time and proper operating conditions and design, the mineralization
efficiency of the AOPs is maximized by optimization of the processes in such a way that the
total costs of the processes are minimized while the removal rates of organic pollutants are maximized.
Since conducting experiments is time-consuming and expensive or sometimes impossible to
do, the modeling of the photoreactors is necessary. Computational fluid dynamics (CFD) is
one of the numerical methods to solve and analyze the transport equations. CFD has been
used recently in order to find the velocity, radiation intensity, pollutant concentration
distribution inside the photoreacotrs (Mohajerani et al., 2010,2011; Qi et al., 2011; Duran et al., 2011a,b, 2010; Vincent et al., 2011; Denny et al., 2009,2010; Elyasi and Taghipour, 2006; Taghipour and Mohseni, 2005; Mohseni and Taghipour, 2004). In this chapter, the velocity
distribution in ten different configurations of single lamp and multi-lamp photoreactors in
both laminar and turbulent regimes are provided. Moreover, the light intensity distribution
inside the photoreactors is also presented.
2. Photoreactor design
The design and analysis of photochemical reactors have attracted researchers’ interests for
the past four decades. The main advantages of the photoreactors over the conventional
thermal excitation reactors are their selectivity and low operating temperature. In spite of these advantages, photoreactors are not widely used in industrial scale. The use of a
photoreactor results in higher product costs; therefore, the photochemical process is used
when there are no other available feasible alternative conventional (thermal or catalytic)
processes. Some other disadvantages such as size limitations, design and construction
difficulties, and fouling on lamp walls have restricted industrial applications of these types of reactors.
Radiation field is the main characteristic of photoreactors determining the kinetics and the photoreactor performance. The photochemical reaction rate is proportional to the local
volumetric rate of energy absorption (LVREA), an important parameter playing a crucial
role in the photoreactor design. The LVREA depends on the radiation field presents within
the photoreactor. The LVREA is a complex function of the lamp intensity, the concentration
of absorbing species, the geometrical characteristics of the photoreactor system, and some
other physicochemical properties. The light attenuation caused by the absorbing species
Computational Fluid Dynamics (CFD) Modeling of Photochemical Reactors
157
makes the LVREA non-uniform. A Photochemical reactor design requires the solution of
momentum, energy, and mass balances. The expression for the conservation of momentum
is similar to that of the conventional reactor. It is believed that light irradiation does not affect the photochemically reactive fluid flow. The mass balance or continuity equations for each compound in the system should be solved simultaneously to find the concentration
profile of each compound inside the photoreactor.
The mass and energy conservation equations are directly related to the light irradiation. The energy balance can be divided into two parts: thermal and radiant energy balances.
Although for isothermal photochemical reactions, thermal balances are negligible, a
complete equation of change for energy balance is required for exothermic and endothermic
reactions. The first step in the LVREA evaluation is to state a radiant energy balance at
steady state condition in a homogeneous system. A radiation source model is also needed to
be considered. Different source models have been developed during the past years to
describe the radiant energy field and to calculate the LVREA.
Gaertner and Kent (1958) were among the first group that modeled photochemical reactions.
They studied the photolysis of aqueous uranyl oxalate in an annular tubular reactor. The
results of their experiments were correlated with a remarkable accuracy by assuming that the rate of photolysis is proportional to the residence time multiplied by the intensity of radiation at a particular radial position. They also proposed a mathematical model without considering the reactant concentration. Therefore, their model was applicable when the conversion was
small (less than 12%). The effect of diffusion was also neglected in their model.
The modeling of radiation field is classified into two categories: incidence and emission
models. In the former approach, a specific radiation distribution exists in the photoreactor, while in the latter approach, the photon emission rate is employed to derive an incidence
model. Although incidence models are mathematically simple to implement, there is no way
of using this approach without experimentally adjustable parameters. Therefore, this
approach cannot be employed as a reasonable systematic method to design photoreactors.
Different incidence models have been developed and used for photoreactor modeling
including radial incidence model (Gaertner and Kent, 1958; Schechter and Wissler, 1960;
Cassano and Smith, 1966, 1967; Cassano et al., 1968; Matsuura and Smith, 1970b, 1971; Santeralli and Smith, 1974; Dolan et al., 1965; Jacob and Dranoff 1969; Williams and Ragonese, 1970), partially diffuse model (Matsuura and Smith, 1970a), and diffuse incidence
model (Jacob and Dranoff, 1969; Williams, 1978; Matsuura et al., 1969; Matsuura and Smith, 1970c; Harada et al., 1971; Roger and Villermaux, 1983).
In emission model, a lamp is considered as an emitting line, a surface, or a volume source.
Different emission models have been developed including line source with parallel plane
emission model (Harris and Dranoff, 1965), line source with spherical emission model
(Jacob and Dranoff, 1966, 1968, 1970; Jain et al., 1971; Dworking and Dranoff, 1978; Magelli and Santarelli, 1978; Pasquali and Santarelli, 1978), and line source with diffuse emission
model (Akehata and Shirai, 1972). Line and surface models are classified into specular and
diffuse emission models. In specular emission, the magnitude of the light intensity vector
is not a function of the emission angle. Photoreactors equipped with mercury arc and neon lamps belong to this class, while fluorescent lamps, in which the magnitude of the
light intensity vectors depend on the angle of the emission, fall into the diffuse emission.
There are some great reviews in which developed models describing the light distribution
in photoreactors are presented in details in the open literature (Alfano et al., 1986a,b; Cassano et al., 1995; Alfano and Cassano, 2009).
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Photoreactors are generally grouped into homogeneous and heterogeneous classes.
Homogeneous reactors operate in a single phase, gas or liquid, in air and water purification systems. In heterogeneous photoreactors, a photocatalyst is added to the system in order to
increase the process efficiency. Heterogeneous photoreactors are subcategorized into
attached (immobilized) or suspended (slurry) modes. Most of the early photoreactors have
employed a titanium dioxide (TiO2) suspension because it offers a high surface area for the
reactions and almost no mass transfer limitation exists in the system. In slurry
photoreactors, a recovery step is necessary to separate, regenerate, and reuse the
photocatalyst. The efficiency of an immobilized system is less than that of the slurry
photoreactor but the photocatalyst is continuously used for a longer period of time.
The disadvantages of the slurry photocatalysis include 1) difficulty and time consuming
process of separation or filtration of the photocatalyst after the photocatalytic process; 2) particle aggregation and agglomeration at high photocatalyst concentration; and 3)
difficulty of using the suspended photocatalyst in continuous processes (Sopyan et al., 1996).
To overcome these drawbacks, immobilized photocatalysts are usually recommended.
Photocatalysts could be immobilized on various supports such as glasses (Sabate et al., 1992; Kim et al., 1995; Fernandez et al., 1995; Wang et al., 1998; Piscopo et al., 2000; Sakthivel et al., 2002; Neti et al., 2010), tellerette packings (Mehrvar et al., 2002), silica (Van Grieken et al., 2002; Ding et al., 2001; Xu et al., 1999; Alemany et al., 1997; López-Muñoz et al., 2005; Marugán et al., 2006), polymers (Kasanen et al., 2009), and clays (An et al., 2008).
The analysis and design of photochemical reactors have received increasing interests in
chemical engineering recently. The photochemical reactors could be used to either produce
and synthesize chemicals or destroy water and wastewater contaminants. The
photochemical reactors are one of the least well known industrial reactors. As mentioned
earlier, the main advantages of the photochemical reactors over the conventional ones are
their selectivity and low reaction temperature. These advantages have become the subject of
several reviews (Doede and Walker, 1955; Marcus et al., 1962; Cassano et al., 1967; Shirotsuka and Nishiumi, 1971; Roger and Villermaux, 1979).
3. Radiation field properties
A bundle of rays with a specific energy carrying photons is called spectral specific intensity and radiance. This parameter plays a detrimental role in radiation field inside a
photoreactor. The spectral specific intensity is defined as the total amount of radiative
energy passing through a unit area perpendicular to the direction of propagation, per unit
solid angle about the direction, per unit frequency, and per unit time. Therefore, the spectral specific intensity unit is Einstein per square meter per stradian, per unit frequency, and per second (Cassano et al., 1995):
dE
I ( x,, t, v)
lim
v
(1)
v
dA, d, dt, dv0 dA cos d d
tdv
Another important photochemical property is the spectral incident radiation that could be
calculated by integrating the spectral specific intensity over the entire photoreactor volume as follows:
G
v
I
(2)
vd
Computational Fluid Dynamics (CFD) Modeling of Photochemical Reactors
159
In spherical coordinates, the spectral incident radiation could be written as follows (Cassano et al., 1995):
2 2
G
I sin
v
(3)
v
d d
1 1
Equation (3) is valid for the monochromatic radiation while for the polychromatic radiation, an extra integration is required as follows (Cassano et al., 1995):
v
2 2 2
G
I sin
v
(4)
v
d d dv
1
v 1 1
The local volumetric rate of energy absorption (LVREA), the absorbed intensity, is the
product of the spectral specific intensity and the absorption coefficient. The rate of a
photochemical reaction is the product of the LVREA and the quantum yield. The quantum
yield indicates the number of moles of chemicals reacted per moles of photons absorbed.
4. Photon transport equation
The photon balance in a photochemical reactor can be written as follows (Ozisik, 1973;
Cassano et al., 1995; Alfano and Cassano, 2008):
timerateof change net flux of , v photons net gainof , v photons owning
of , v photonsin leavingthevolume
to emission, absorption, in – scattering,
(5)
thevolume
acrossthesurface A
and out – scattering in
the volume
The right hand side of Equation (5) could be divided into two sources (emission and in-
scattering) and two sink (absorption and out-scattering) terms, therefore, the photon balance equation could be written as follows (Cassano et al., 1995):
I
1 , v .
em
in s
ab
out s
I
(6)
, v
W W
W
W
, v
, v
, v
, v
c
t
The absorption and emission terms are useful for both homogeneous and heterogeneous
photochemical reactors. The loss of photons due to the absorption could be calculated using
the following expression (Cassano et al., 1995):
ab
W
K ( x, t) I ( x,, t) (7)
, v
v
v
where Kv is the absorption coefficient, which shows the fraction of the incident radiation that is absorbed by the molecule per unit length along the path of the beam. The emission term
highly depends on temperature as shown in Equation (8). Photolytic and photocatalytic
reactors usually operate at low temperatures, therefore, this term can be neglected for
photoreactor modeling:
em
W
K ( x, t) I
T
( x, t)
(8)
,
v
v,
v
b
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Applied Computational Fluid Dynamics
The following two equations account for the gain and loss of photons due to in-scattering
and out-scattering, respectively (Cassano et al., 1995). In homogeneous photoreactors, these two terms (in-scattering and out-scattering) are neglected due to the absence of
semiconductors:
s in
1
W
(9)