Simulation of cement clinker process by of microwave heating José Pedro Machado Mendes Thesis to obtain the Master of Science Degree in Mechanical Engineering Supervisors: Prof. José Carlos Fernandes Pereira Dr. Duarte Manuel Salvador Freire Silva de Albuquerque Examination Committee Chairperson: Prof. Carlos Frederico Neves Bettencourt da Silva Supervisor: Dr. Duarte Manuel Salvador Freire Silva de Albuquerque Member of the Committee: Prof. Viriato Sérgio de Almeida Semião June 2017
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Simulation of cement clinker process by of microwaveheating
José Pedro Machado Mendes
Thesis to obtain the Master of Science Degree in
Mechanical Engineering
Supervisors: Prof. José Carlos Fernandes PereiraDr. Duarte Manuel Salvador Freire Silva de Albuquerque
Examination Committee
Chairperson: Prof. Carlos Frederico Neves Bettencourt da SilvaSupervisor: Dr. Duarte Manuel Salvador Freire Silva de AlbuquerqueMember of the Committee: Prof. Viriato Sérgio de Almeida Semião
June 2017
ii
Dedicated to my grandfather, who didn’t make it to see his grandson graduate.
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Acknowledgments
I would like to start by thanking to my supervisors Prof. Jose Carlos Fernandes Pereira and Dr.
Duarte Manuel Salvador Freire Silva de Albuquerque for their guidance and orientation. And specially
to Dr. Duarte for his friendship, dedication, sacrifice and availability.
I would like to thank my colleagues at Laboratory of Simulation in Energy and Fluids (LASEF) for
their companionship.
Finally i would like to give a special thank to my beloved family and friends for their unconditional
comprehension and support during the preparation of this document.
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Resumo
A producao convencional de clınquer de cimento e um processo que requer bastante energia, ne-
cessitando de 3600 kJ para obter um unico quilograma. Alem disso, uma vez que e um dos materiais
mais utilizados no mundo, a sua producao representa ate 6% do total de CO2 emitido pela atividade
humana. A tecnologia de aquecimento por via de micro-ondas tem ganho interesse como uma alter-
nativa devido as suas vantagens. E uma energia limpa e sem emissoes diretas de CO2, ao contrario
do aquecimento convencional. Aquecimento por micro-ondas ocorre quando o campo eletrico interage
com o material, resultando num aquecimento volumetrico no interior do material, o que se traduz em
maiores eficiencias.
Esta Dissertacao aborda o tema do aquecimento por micro-ondas na producao de clınquer de ci-
mento, mais especificamente, na calcinacao de calcario. O objetivo inicial e validar as capacidades do
COMSOL no tratamento dos fenomenos fısicos envolvidos. Este programa provou ser uma ferramenta
adequada para prever os processos quımicos e o comportamento de um plasma induzido por micro-
ondas. Em seguida, propoe-se um novo algoritmo capaz de, autonomamente, simular uma unidade de
processamento de calcario com uma elevada eficiencia global. Este algoritmo e capaz de fazer os ajus-
tamentos necessarios na potencia imposta e no estado de ressonancia da cavidade de micro-ondas,
conseguindo assim, obter uma total conversao de calcario e evitando problemas relacionados com a
temperatura. Por fim, esta metodologia apresentada mostra melhoramentos significativos, face a outros
modelos numericos do genero existentes na literatura.
Palavras-chave: Modelo numerico de aquecimento por micro-ondas, Correspondencia au-
tomatica de impedancia, Otimizacao de potencia imposta, Producao de clınquer de cimento, Processa-
mento contınuo de calcario por micro-ondas.
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Abstract
Conventional cement clinker production is a very energy demanding process, that requires up to
3600 kJ for a single kilogram of cement clinker. Moreover, since it is one of the most used materials in
the world, its production accounts for up to 6% of the total CO2 emitted by the human activity. Microwave
heating technology has been gaining interest as an alternative for its advantages. It is a clean energy
with no direct CO2 emissions, and, unlike conventional heating, microwave heating happens when the
electric field interacts with the material, resulting in a volumetric heating inside the material, returning
higher efficiencies than the conventional counterpart.
This Thesis addresses the subject of microwave heating in the production of cement clinker, specifi-
cally in the limestone calcination. The initial goal is to validate capabilities of COMSOL in handling all the
physical phenomena involved. This software has been proven to be a suitable tool to predict chemical
processes and the behavior of a microwave induced plasma. Afterwards, a new method is proposed
and a code developed that can autonomously simulate a limestone processing unit with overall high
efficiency, using microwave energy. The code is capable of making the necessary adjustments to the
input power and resonant state of the microwave system, and was able to achieve total conversion of
limestone, while maintaining high efficiency and avoiding temperature related problems. As such, the
presented methodology shows a significant improvement over other available numerical models in the
literature for microwave heating.
Keywords: Microwave heating numerical model, Automatic impedance matching, Input power
Alpert and Jerby [41] created a one dimensional model to study microwave heating of temperature
dependent dielectric materials though the two-way coupling of the thermal and electromagnetic fields.
The models resorted to FEM and two different time scales were used to reduce computational time.
Two separate diffusion functions were also derived in order to obtain more accurate temperature and
electromagnetic distributions. The developed model was successfully benchmarked against other works,
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and the predicted temperature profiles allow to avoid thermal runaway. Zhu et al. [42] proposed a
mathematical model for microwave heating of liquids with a particularity of considering a continuous flow
rather than a stationary sample. Apple sauce, skim milk and tomato sauce flowed through a circular duct
which was bombarded with microwave radiation. The objective was to investigate the effect of dielectric
properties of the liquids, the dimensions and location of the circular duct as well as investigate the cavity
design. A finite difference time domain method was chosen to compute the electromagnetic field and,
through the obtained results, Zhu et al. [42] observed how the heating is strongly dependent on the
material’s dielectric properties and on the geometry of the microwave cavity.
Among others, authors such as Salema and Afzal [10] and Mimoso et al. [11] resorted to COM-
SOL to tackle their studies. Salema and Afzal [10] simulated microwave heating of stationary samples
of biomass, in bed and pellet form, in a multimode microwave oven and validated against experimen-
tal studies. It was showed that temperature and heating behavior of the samples are affected by the
biomass loading height and specific heat capacity. The obtained results allowed for the evaluation of the
optimal biomass loading height for a particular set of microwave power and frequency, where maximum
microwave energy absorption could be attained. Moreover, the model can be successfully used to iden-
tify hot and cold spots in the samples during the heating process, enabling the possibility of optimizing
the design of the microwave heating systems regarding uniformity. The work developed by Mimoso et al.
[11] consisted of a continuous glass melting in a single mode microwave cavity at 2,45 GHz. The main
objective of the conducted study was to optimize the microwave processing of glass while maintaining
high levels of energy efficiency and avoiding thermal related problems. Phase change from solid to liquid
in the glass region was included, as well as surface to surface radiation. A MATLAB code was devel-
oped to microwave power input and to maximize material’s energy absorption during the course of a 3D
transient simulation. The developed methodology was able to achieve high energetic efficiency while
maintaining specific power as low as possible. Through the obtained results, Mimoso et al. [11] were
able to conclude that, in order to maintain and high efficiency inside the cavity, a plunger adjustment to a
more efficient position is continuously required at specific times. Moreover, it was seen that pre-heating
the material at the inlet reduced global efficiency as it increased thermal losses due to radiation and
convection. Hence, when steady state is achieved pre-heating is turned out to be undesirable, however
pre-heating the whole material at the beginning of the process helps starting the heating process faster
and with more efficiency.
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Chapter 2
Background
This chapter is dedicated to introduce the reader to the governing equations and important concepts
of the various phenomena discussed in this Thesis.
2.1 Maxwell’s equation
Maxwell’s equations depict the interactions between the electric and magnetic field at a macroscopic
level. These equations are based on other’s empirical and theoretical knowledge, namely Faraday,
Gauss and Ampere. The differential form of these equations are presented next. A more in-depth
explanation of the Maxwell’s equations and the equivalent integral form can be found in many textbooks
such as in Popovic and Popovic [43].
∇× ~E = −∂~B
∂t(2.1)
∇× ~H =∂ ~D
∂t+ ~J (2.2)
∇ · ~D = ρq (2.3)
∇ · ~B = 0 (2.4)
Where:~E is the electric field, in volts per meter (V/m);~B is the magnetic flux density, in webers per squared meter(Wb/m2);~H is the magnetic field, in amperes per meter (A/m);~D is the electric flux density, in coulombs per squared meter (C/m2);~J is the electric current density, in amperes per squared meter (A/m2);
ρq is the electric charge density, in coulombs per cubic meter (C/m3);
t is time, in seconds (s).
Equation 2.1 is Faraday’s law of induction. It is the cornerstone of electromagnetism and constitutes
an example of the profound connection between ~E and ~B and it states that time variation in the magnetic
9
field has a correspondent spatial variation in the electric field. Equation 2.2 is the Ampere’s law. From it
one knows that a variation in the electric field causes a change in the magnetic field. The electric current
density term ( ~J) is the responsible for the creation of a magnetic field that circles the electric current.
Equation 2.3 is the Gauss law. It expresses how the electric field behaves around electric charges and
it states that the divergence of the electric flux density, over any region of space, is equal to the charge
density. Finally, equation 2.4 is Gauss law for magnetism. Looking to equation 2.3 it is possible to
see the similarity, being the difference the field in the divergence operator. In this case we have the
divergence of the magnetic flux density and it is expected to be equal to the magnetic charge (the same
way eq. 2.3 is equal to the electric charge). However, so far, there is no evidence that magnetic charges
do exist and thus the divergence of ~B equals zero, and so, no second term is visible in equation 2.4.
Through some algebraic manipulation it is possible to deduce another relation from Maxwell’s equa-
tions. Knowing that ∇ · (∇ × ~H) = 0 (divergence of the curl of any vector field is equal to zero) one
can substitute equation 2.2 into it. Then, using the relation established in equation 2.3 the continuity
equation of energy can be derived:
∇ · ~J +∂ρq∂t
= 0 (2.5)
To fully describe the fields involved in electromagnetism additional relations need to be added to
Maxwell’s equations. This are called constitutive equations and establish the relations between the vec-
tor entities seen in the above Maxwell’s equations. These equations depict the macroscopic properties
of the material medium where the electromagnetic field exists.
~D = ε ~E (2.6)
~B = µ ~H (2.7)
~J = σ ~E (2.8)
Where ε, µ and σ are the constitutive parameters of the material medium: ε is the permittivity (F/m), µ is
the permeability (H/m) and σ is the electrical conductivity (S/m). The equations are written for a linear
isotropic and homogeneous medium. Equation (2.8) is the vectorial form of te Ohm’s law.
Sometimes it is useful to form problems in terms of the magnetic and electrical potential, respectively~A and φ. As such, it is necessary to establish the respective general relations between ~B and ~E and the
respective potentials introduced above:
~B = ∇× ~A (2.9)
~E = −∇φ− ∂ ~A
∂t(2.10)
As stated above, the Maxwell’s equations (eqs. 2.1 to 2.4) are partial differential equations having
time and the spatial coordinates as independent variables. However it is frequent to have a sinusoidal
time variation of the sources. Plus if the medium is linear, we can conclude that all quantities have
10
a sinusoidal variation in time. So, taking it all into account, time can be removed form the equations
simplifying them in the process. Sinusoidal time dependent quantities can have their time dependence
written in the form:
cos(ωt+ ϕ) (2.11)
With ω = 2ϕf being the angular frequency (in rad/s), f the frequency (in Hz), and ϕ the initial phase.
So considering ~X a time-harmonic field, it can be expressed as follows:
~X = ~X0 cos(ωt+ ϕ) (2.12)
Resorting to Euler’s formula it is possible to write the cosine as a sum of complex exponentials with
j =√−1:
cos(ωt+ ϕ) =exp(j(ωt+ ϕ)) + exp(−j(ωt+ ϕ))
2(2.13)
The variables presented in Maxwell’s equation can all be represented resorting to this relation, and
so it is common to replace the cosine for exp(jωt). Hence, to represent the derivative of a sinusoidal
quantity in respect to time it just needed to replace the time derivative with jω [43].
According to this formulation it is now possible to write Maxwell’s equations in the complex (or phasor)
form resulting in fields possessing both real and complex part as can be seen below.
∇× ~E = −jω ~B (2.14)
∇× ~H = ~J + jω ~D (2.15)
∇ · ~D = ρq (2.16)
∇ · ~B = 0 (2.17)
2.2 Complex Permittivity
The microscopic behavior of a material subjected to an external field is generally dependent on
the field’s frequency. This dependence is a reflection of the non-instantaneous response to an applied
field by the material’s polarization. The response gives rise to a phase shift difference between the
polarization (~P , in (C/m2)) and the electric field ( ~E). This behavior can be analytically represented by
means of a complex permittivity, ε, as follows:
ε = ε′ − jε′′ (2.18)
The permittivity of dielectric materials can then be normalized to that of free space:
ε′ = ε0ε′r ; ε′′ = ε0ε
′′r (2.19)
Where ε0 = 8.85× 10−12 (F/m) is the free space permittivity, and so the complex relative permittivity is
11
represented as follows:
εr = ε′r − jε′′r (2.20)
Permittivity describes the interaction of the material with the electric field [44] and these interactions
can happen in one of two distinct ways: energy storage and energy dissipation. Energy storage de-
picts the lossless energy exchange between the electric field and the material, while energy dissipation
happens when the energy is absorbed by the material. Regarding equation (2.20) the capacity of the
material to store energy is translated by the real part of the complex permittivty (ε′r) which it is known
as dielectric constant and is responsible for phase shift of the electric field and storing its energy. On
the other hand, the capability of the material to dissipate energy, one of the most important properties
for microwave heating, is represented by the imaginary part of the same equation (ε′′r ) which is called
the loss factor and is responsible for the electric energy losses that are transformed into heat. In a
qualitative form, the time-varying field induces time-varying dipoles in the dielectric, as such, it starts to
vibrate more vigorously due to these variations which result in heat [43]. A similar demonstration to the
one presented above can be made for permeability.
The complex permittivity depends upon the frequency and temperature. Regarding the frequency,
for different ranges, the material will have distinct responses which correspond to various phenomena.
The major mechanism that contribute to the permittivity of a certain dielectric material are the ionic
conduction, dipolar relaxation, atomic polarization and electronic polarization as can been seen in Fig.
2.1. It is noteworthy to highlight that dipolar relaxation is the major cause for permtittivity variation in the
microwave range of frequencies.
Figure 2.1: Frequency dependence of permittivity for a hypothetical dielectric material [45].
In respect to temperature dependence, it is usually subject of more focus as frequency of the source
is fixed to one value in most applications [8]. From the literature, it is known that there is an increase
of the loss factor when increasing the temperature [8], however in some materials this increment is
greater than others [46], which can lead to some unwanted problems. What happens is that the initial
12
microwave energy will be absorbed and temperature will increase causing ε′′ to increase, and as a result
temperature will rise again and so on.
2.3 Microwave Rectangular Waveguide
A brief description of a rectangular waveguide is the topic of this section as it is used in all of the
studies conducted in this work. A waveguide is a structure that is able to conduct electromagnetic energy
along a determined path. Although waveguides can be of various shapes and forms, we will be focused
in studying waveguides in the form of hollow metallic tubes, and in particular the rectangular shaped
ones, as the one seen in Figure 2.2 where a is the largest dimension of the waveguide (a > b).
Figure 2.2: Schematic of a rectangular waveguide.
The rectangular waveguide can propagate Transverse Magnetic (TM) and Transverse Electric (TE)
modes, but not Transverse Electromagnetic (TEM) modes as only one conductor is present [47]. Elec-
tromagnetic waves are transversal waves. In Transverse Electric modes there is no electric field in the
direction of propagation, and it is characterized by Ez = 0. The Transverse Magnetic mode is charac-
terized by Hz = 0, so there is no magnetic field in the direction of propagation. In the case of the TEM
mode, there is no electric nor magnetic fields in the direction of propagation, as they are both transversal
to it.
2.3.1 TE Mode
According to Pozar [47], assuming time-harmonic fields and using the separation of variable meth-
ods, it is possible to obtain the equations for the electromagnetic field of a TEmn mode propagating in a
rectangular waveguide, filled with a material of permittivity ε and permeability µ, as follows:
13
Hx =jβmπ
k2caAmnsin
mπx
acos
nπy
be−jβz (2.21)
Hy =jβnπ
k2cbAmncos
mπx
asin
nπy
be−jβz (2.22)
Hz = Amncosmπx
acos
nπy
be−jβz (2.23)
Ex =jωµnπ
k2cbAmncos
mπx
asin
nπy
be−jβz (2.24)
Ey =−jωµmπk2cb
Amnsinmπx
acos
nπy
be−jβz (2.25)
Ez = 0 (2.26)
In the previous equations Amn is an arbitrary amplitude constant that depends on the level of excitation
of the wave [47] and β is the propagation mode which is expressed as follows:
β =√k2n − k2c =
√k2n −
(mπa
)2−(nπb
)2, (2.27)
with kc being the cutoff wave number and kn = ω√µε the wave number. The parameter β corresponds
to a propagating mode when it is real, and that happens when kn > kc.
For each TE mode there will be a correspondent cutoff frequency as expressed by (2.28), which is
the lowest frequency for which a mode will propagate in a waveguide with section axb. A wave with a
frequency under this value will see its fields decay as it travels along the waveguide.
fcmn=
kc2π√µε
=1
2π√µε
√k2n −
(mπa
)2−(nπb
)2(2.28)
The TE mode for which we have the lowest cutoff frequency is called fundamental mode (or dominant
mode). This mode (assuming a > b) will be the TE10 mode (with m = 1 and n = 0) and its cutoff
frequency is:
fc10 =1
2a√µε
(2.29)
Usually, in the majority of waveguide applications, the dimensions and frequency of operation are
chosen in order to only allow the TE10 mode to propagate. Hence, and due to their importance, equa-
tions (2.30) to (2.33) describe the electromagnetic field of this mode inside de waveguide (with m = 1
and n = 0).
Hz = A10cosπx
ae−jβz (2.30)
Ey =−jωµaπ
A10sinπx
ae−jβz (2.31)
Hx =jβa
πA10sin
πx
ae−jβz (2.32)
Ex = Hy = Ez = 0 (2.33)
The cutoff wave number and the propagation constant for this mode can then be expressed respec-
14
tively as:
kc =π
a; β =
√k2n − (π/a)2 (2.34)
Finally, the wave impedance (ZTE) and the guide wavelength (λg) can also be introduced [47][43]:
ZTE =ExHy
=knη
β=
√µ/ε√
1− f2c10/f2(2.35)
λg =2π
β=
λ0√1− f2c10/f2
(2.36)
Where λ0 is the wavelength of a plane wave with the same frequency and in the same considered
medium [43] and η =√µ/ε is the intrinsic impedance of the material that fills the waveguide.
2.3.2 TM Mode
Taking an identical approach as in the TE mode and recalling that TM modes are characterized by
having Hz = 0, the field components for a TMmn mode can be presented:
Hx =jωεnπ
k2cbBmnsin
mπx
acos
nπy
be−jβz (2.37)
Hy =−jωεmπk2ca
Bmncosmπx
asin
nπy
be−jβz (2.38)
Hz = 0 (2.39)
Ex =−jβmπk2ca
Bmncosmπx
asin
nπy
be−jβz (2.40)
Ey =−jβnπk2cb
Bmnsinmπx
acos
nπy
be−jβz (2.41)
Ez = Bmnsinmπx
asin
nπy
be−jβz (2.42)
In the previous equation Bmn is an arbitrary amplitude constant like Amn was for the the TE mode.
For the TM modes the propagation constant and cutoff frequencies assume the same formulas as the
ones seen for the TE mode (equations 2.27 and 2.28 respectively). The waveguide length (λg) is also
the same as it was for the TE mode (equation 2.36), while the impedance assumes the following form:
ZTM =ExHy
=βη
kn(2.43)
2.4 Heat Transport Equation
The following equation (2.44) describes the heat transfer phenomenon, ignoring the pressure work
and the viscous heating. Its solution will give the temperature field.
ρcp∂T
∂t+ ρcp~u · ∇T = ∇ · κ∇T +Q (2.44)
where ρ is the density (kg/m3), cp is the specific heat capacity (J/(kg ·K)), u is the velocity vector
15
(m/s), κ is the thermal conductivity (W/(m · K)), T is the temperature (K) and Q (W/m3) is the heat
generation term (W/m3). In microwave heating this last term Q represents the coupling of Maxwell’s
equations with the heat equation and is the sum of the power dissipated by Joule effect and the dissipa-
tion of the electromagnetic power (due to the presence of a material with the dielectric loss effect) and
can be represented by the following equations:
Qj = σ|E|2 (2.45)
Qdiss = ε0ε′′rω|E|2 (2.46)
Regarding equation (2.46), recall that it expresses the energy deposition phenomenon that results
from the alternating electric field in a medium with dielectric loss properties [46]. Further, note that it
includes the dielectric loss factor ε′′r which is responsible for the electromagnetic energy dissipation that
is transformed into heat, as discussed in section 2.2.
Furthermore, it is now necessary to attend the cement clinker and plasma domains regarding this
matter. To what the cement clinker is concerned, the heat generated and absorbed by the chemical
reactions that take place need to be added to the microwave heat generation term, and so Q turns out
to be the sum of two heat generation terms: one related to the heat coming from the chemical reactions
(one for each reaction), as seen in equation (2.47); and another to the microwave heating. Finally, in
the plasma domain, to the heat coming form the microwave heating generation term, it is necessary to
take into account and add the heat that is transfered from the free electrons of the plasma to the heavy
species present in it, translated through equation (2.48) [37]. Hence, the term Q of the heat equation
will be the added contributions of all these mechanisms depicted.
Qreact = ∆H Rreact (2.47)
Qel = 3me
MkBνeN (Te − T ) (2.48)
In equation (2.47), ∆H is the enthalpy change for a given reaction and Rreact is the reaction rate for
a given reaction. The meaning for the variables of equation(2.48) can be found on section 2.7.
In the electron energy density equation (2.57), nεp stands for the electron energy density (V/m3) and
Rεp represents the energy loss/gain due to inelastic collisions (V/(m3 · s)). Regarding equation (2.58),~Γεp is the electron energy flux, µεp is the electron energy mobility (m2/(V · s)) and Dεp is the electron
energy diffusivity (m2/s).
Due to their high mobility and low mass, electrons are the first to receive energy from the electric
fields. This energy is then transfered to the other plasma components giving the required energy for
the plasma-chemical processes to occur (ionization, excitation and dissociation) [40]. The rate of those
processes depend on the amount of electrons that have the energy to start them. This energy can be
depicted by resourcing to the electron energy distribution function (EEDF) f(εp), which is the probability
density for an electron to have its value of energy equal to εp. The electron diffusivity, energy mobility
and energy diffusivity can be calculated by using Einstein’s relation for a Maxwellian EEDF (there are
other distributions besides the Maxwellian but only this one is used in studies conducted) such that:
De =kBTee
µe (2.59)
µεp =
(5
3
)µe (2.60)
Dεp =kBTee
µεp (2.61)
µe =e
meνeN(2.62)
In the previous equation kB is the Boltzmann constant (1.386488(13)× 10−23J/K), e the electron charge
(−1.602× 10−19C), me is the electron mass (9.109× 10−31kg) and with νeN being the collision frequency
between electrons and Neutrals. The EEDF can then be used to calculate reaction rates coefficients
of plasma-chemical processes involving electrons (electron impact reactions and electron attachment
21
reactions):
kk =
(2e
me
)1/2 ∫ ∞0
εpσk(εp)f(εp) dεp (2.63)
In equation 2.63 σk is the collision cross section. Collisions cross sections for several reactions are
available in many references of the literature [53] and databases [54]. However these reactions rates
can also be defined by inputing a specific forward rate constant coefficient.
The mean electron energy ε (eV ) and the electron temperature Te (eV ) can be calculated from:
εp =nεpne
(2.64)
Te =
(2
3
)εp (2.65)
2.7.2 Heavy Species Transport and Plasma Properties
The heavy species in a plasma are the neutral, excited and ionized components that take part in
it. The transport equation is equation (2.52) seen in the section (2.6.1). As in section (2.6.1) i − 1
species are possible to solve, and the mass fraction of the remaining species is computed from the
mass constraint. To calculate the source coefficients (Ri) it is possible to just specify a forward rate
constant coefficient directly or, again, use the Arrhenius Law as described in (2.6.2) to compute the
reaction rate. It is however common to use the modified version of the Arrhenius equation as it explicits
the temperature dependence of the pre-exponential factor.
k = k0Tne−Ea/(RT ) (2.66)
In equation 2.66 n typically ranges between −1 < n < 1. it is convenient to also present a way to
determine the number density of a certain species i as it will be useful in the studies regarding plasmas,
ni =
(p
kBT
)xi, (2.67)
where p stands for pressure and xi for the mole fraction of the species i.
Finally and regarding the plasma mixture itself, there are still some variables of great importance yet
to be introduced. Namely the electrical conductivity, σ, the relative electrical permittivity, εr [37] and the
gas heat capacity, Cp [39], all presented in equations (2.68) to (2.70) in the same order while the Plasma
density is computed through the ideal gas law as in equation (2.71).
σ =nee
2
me
1
νeN(2.68)
εr = 1− nee2
ε0me
1
(ωf − jνeN )(2.69)
Cp =5kB2M
(2.70)
ρ =pM
RT(2.71)
22
With M being the mole averaged molecular weight (kg/mole) and ω the angular frequency (ω = 2πf ).
i. If the maximum efficiency is found for the current position leave loop 2;
ii. If not, run a new frequency domain simulation for the plunger position that returned the
highest efficiency and for the its two neighboring positions;
(g) Compute the new power input required from the data extracted at (c) using equation (4.12);
(h) If transient term of the energy balance equation and the average percentage of reactant at
the quartz tube exit are ≤ 1 and < 1.5% respectively, leave loop 1;
(i) If the new power input is greater than the power input at the end of the previous simulation,
then the new power is linearly increased during the course of the new transient simulation;
(j) if the new power input is lower than the previous onde, then the new power input is established
in its full magnitude at the beginning of the new transient simulation;
4. End of the MATLAB code and the last solution is the converged one for the set of parameters of
velocity and inlet temperature.
4.5 Initial energy testing model
Before initiating a fully coupled simulation between the three physics involved a test was made to
assess if the model was operating as expected from a chemical standpoint and its interaction with the
thermal interface. An energy balance has to be made in order to check if the energy input is being
conveyed to the right places. This study was conducted considering only the chemical and heat transfer
interfaces so that simulation time is reduced when compared to a fully coupled one. To simulate the
microwave power deposition, an artificial heat source is imposed in the material bed domain.
The mass flow of limestone is set to 0.75 kg/h. A transient study is conducted until the integral of the
temporal term of the energy equation is converged and the limestone is converted at the exit. Meaning
little temperature variations over the whole model and that the simulation has reached steady state. A
steady state situation is achieved for a power of 640 W and a residual mass fraction of 0.5% of CaCO3 is
still present at the tube’s exit so a complete conversion of the reactant can be considered.
50
Through figures 4.12 and 4.13 it can be attested the interconnection between the temperature and
the CaCO3 (limestone) conversion. Regarding the energy balance, table 4.5 refers to the extracted data
used to compute the balance and summarizes the power usage and losses of the model.
Figure 4.12: 2D cut on the ZX plane of the temperature field of the testing model.
Figure 4.13: 2D cut on the ZX plane of the CaCO3 mass fraction of the testing model.
Convective losses 233.35W
Material’s exit energy 45.5W
Endothermic reaction heat source ) + 372.65W
Total used energy = 651.5W
Power input 640W
Table 4.5: Energy balance of the initial model tested.
In table 4.5, the convective losses are computed using the equation (4.5). The energy lost through
the material exiting the tube is known resorting to the second term of equation (4.12). The endothermic
reaction heat source is computed by integrating equation (4.4) over the entire volume of the bed domain.
As can be seen the total amount of power lost to the various processes sums up to 651.5W . Facing
the computed value with the input power of 640W referred above, an 1.76% difference can be spotted
which is fairly reasonable. Other important value to take into account is the endothermic reaction heat
source imposed at the bed material domain. It presents a value of 372.65W which is roughly the same
as the theoretical one of 372.05 W computed by multiplying the converted mass flow by the energy of
the reaction (1795 [kJ/kg]). Hence it is possible to conclude that the power absorbed by the chemical
reaction is being well computed.
51
4.6 Results
4.6.1 Limestone processing
In the present section the aim is to expose and discuss the results obtained from the simulations car-
ried out. It is the culmination of the process that has been presented so far. The operational parameters
have already been discussed, however, for convenience they are recalled in table 4.6.
Operational parameter Value
Initial bed temperature 900K
Remaining model initial temperature 293K
Material’s inlet temperature 293K
Mass flow rate 0.25 kg/h
Table 4.6: Operational parameters.
From the presented mass flow, power input for the first simulation step is computed according to
equation 4.12 giving approximately 125 W of power to be delivered by the microwave source. Plunger
will be set at a distance of 144 mm from the tube’s center as previously addressed and the simulation
time is set to be 1/4 of the residence time, and so it is adjusted to 1512 seconds.
From figures 4.14, 4.15, 4.17 and 4.18 it is possible to observe the major variables obtained through
the control algorithm implemented in MATLAB. They enable the evaluation of the conditions on which
the model is operating and allow for the MATLAB controller to intervene and adjust power and plunger
position as suitable until a steady state status is attained. Figure 4.16 presents the thermal distribution
evolution through the simulation at key time points marked in 4.15 respectively. Table 4.7 summarizes
the following set of five figures in order to give an initial brief understanding about the content of each
one, due to the interconnection of the data presented between them. The whole simulation process
required 9 transient studies in order to achieve a steady state for a total simulated time of 13 608
seconds corresponding to roughly 3 hours and 46 minutes of computing time.
Figure Content
Figure 4.14 Controlling variables of the MATLAB algorithmFigure 4.15 Temperature evolutionFigure 4.17 Chemical evolutionFigure 4.18 Energy balanceFigure 4.16 Thermal field distribution evolution at key time points
Table 4.7: Limestone processing figure’s content.
In figure 4.14, access is given to the evolution of the microwave efficiency, plunger position, power
input and the stored heat rate which is the transient term from the energy equation 2.44. It is possible
to notice that in the first time interval (0s-1512s) the efficiency drops dramatically although the plunger
positions is spot on (because initially efficiency is high). This happened mainly due to the low input
power of around 125 W set in this stage. As power is not enough to overcome the convection losses
52
Figure 4.14: Stored heat, power input, microwave efficiency and plunger position evolution during thesimulation time.
throughout the bed domain and hence to maintain the material’s temperature, as can be seen in figure
4.15, where temperature falls till point (a) with the temperature distribution presented in 4.16 (a), the
dielectric properties will change due to this temperature drop. As a result, with a lower dielectric loss
distribution the capacity of the material to absorb the microwave radiation is also diminished, and so, the
microwave efficiency is reduced. The stored heat rate represents the state of cooling or heating of the
model, in this case this variable drops from zero to a negative value, as can be spotted, indicating that
the materials’ temperature is dropping.
For the second time interval (1512s-3024s) a new plunger position is obtained and the input power
is update according to 4.12. As can be noticed, the new power input is not established right away,
instead it is linearly increased from the beginning to the end where it reaches the computed power.
Although this increases the whole simulation time, it helps with the stability and diminishes the chances
of temperature related problems, from sudden increases in energy absorption (increased efficiency)
before the controller intervention. At the end of this time interval an example of such event is present,
as it can be attested in figure 4.15 in the maximum temperature line. However, due to lower power input
in the next time interval this effect was mitigated. For the remaining time intervals the model suffers less
changes, and minor adjustments in power are done until steady state and total conversion (see figure
4.17) are obtained. Steady state is obtained when the stored heat rate reaches zero, this means that
the transient term of equation (2.44) is negligible and that no overall temperature changes are occurring
in the model.
As the bed material is the only capable of absorbing significant amounts of microwave energy, it is
53
safe to say that the power input multiplied by the microwave efficiency returns the power absorbed by the
bed which is represented in figure 4.15. In this figure the maximum temperature recorded on the material
bed and the mean material temperature at the outlet are also under display. From careful observation
it is possible to notice the strong coupling between the thermal field and the microwave interface. With
the increase in power absorption (due to the increase in input power) a higher maximum temperature is
obtained, as a consequence, the dielectric loss factor increases, and so, it will allow for a better power
absorption and increased efficiency. This feedback loop will develop a steeper slope of the maximum
bed temperature and absorption power through points (a), (b) and (c) in figure 4.15. This phenomenon,
although useful cause it accelerates the process, if not contained, can lead to the already discussed
problems of hot spots or thermal runaway.
Figure 4.15: Bed power absorption, maximum bed temperature and outlet bed temperature versussimulation time.
In figure 4.16 the thermal field distribution corresponding to the time instances marked in figure 4.15
can be found. With these distributions it is possible to discuss how the coupling affects the present
results, specially the feedback mechanism between the temperature and electric fields. From (a), (b)
and (c) one can see the consequence of power deposition to the warmer areas, making those areas
hotter and smaller. If no measures were taken at moment (c) the hot spot would only get hotter and
more concentrated absorbing the majority of the input power. Figure (d) is displayed to give an insight to
the temperature distribution at steady state. As it is possible to observe, the concentrated hot area of the
previous time mark has dissipated, becoming wider and better distributed. The mean outlet temperature
of the material is presented in figure 4.15 as to show its relation to the maximum temperature. It behaves
54
(a) Time=1512s; Max. Temperature:487 K. (b) Time=2268s; Max. Temperature:553 K.
(c) Time=3024s; Max. Temperature:1154 K. (d) Steady state (13608s); Max. Temperature:1123 K.
Figure 4.16: Evolution of the thermal field over the course of the limestone processing simulation.
just as expected being a key variable when computing the power input for each time interval as verified
by equation (4.12).
With the temperature increase, temperature dependent chemical processes are expected to occur.
The interconnection between the thermal field and the chemical interface is briefly presented in figure
4.17. It is possible to verify that with temperature increase the endothermic reaction begins to convert
limestone into lime and the respective heat source starts to increase. The endothermic reaction is
considered to hold according to Arrhenius law, which as previously seen, is temperature dependent. The
Arrhenius term ”K” will increase resulting in a higher reaction rate. As conversion proceeds, CaCO3
will decrease which results in a reduce in pace of the reaction rate until it reaches total conversion,
explaining the behavior of the limestone mass fraction. The reaction heat source will absorb energy
from the system (endothermic) and its evolution depends on temperature due to the connection with the
reaction rate (equation 2.47). As it is possible to see it gets triggered when the reaction begins to take
place. Later, at steady state, the heat source stabilizes to a fixed value corresponding to the energy
required to convert the limestone that flows through the tube.
The objective in the displayed information of figure 4.18 is to present the evolution of the energy
consumption and losses. Energy consumption happens though the present chemical reaction, on the
other hand, energy losses are portrayed by convection losses and enthalpy loss trough the tube’s outlet.
However, not all losses can be technically considered as losses. In order to start the reaction, a certain
temperature must be met (around Treact=1073K), thus, it is required energy to heat the material up to
that temperature according to equation 4.13. If the system were to be adiabatic the outlet temperature
would be the reaction temperature. Yet, it is not. That means, that some of the heating enthalpy was
lost through convection and did not leave the system by the tube’s outlet. That means, the convection
losses will be the value obtained from COMSOL subtracted by the difference between the heating power
(Pheat) and the enthalpy of the material at the tube’s outlet
Pheat = mflowCp(Treact − Tin) (4.13)
55
Figure 4.17: Limestone mass fraction, maximum bed temperature and reaction heat source versussimulation time.
Figure 4.18: Bed power absorption and power losses/usage versus simulation time.
As it is possible to notice, all the power usage and losses are conveniently presented in absolute values
and their summation without the stored heat rate is also given as to compare it to the power absorption.
56
It can be seen that the difference between sum of the power usage line and the bed power absorption
line is the stored heat energy. The bigger the difference, the farthest away from steady state the system
is. As efficiency increases so does power absorption, and after a while, power losses start to increase
and catch up. At steady state it is possible to observe a balance between the power that is absorbed,
the one being used and the one that is lost, while the stored heat is negligible. This helps to conclude
that the majority of the energy of the model is being accounted for.
In figure 4.19 an energy balance for the steady state is presented in order to complement the previous
information. The absorbed power accounts for 84.6 % (301 W) of the input power (356 W) while 15.4 %
of it is reflected back. The thermal losses are constituted by the convection losses, and, accounting the
energy that leaves the tube through the outlet material, it adds to roughly half of the total input power
in the model. The power used to heat the material up to the reaction temperature is computed using
equation (4.13), returning 43.4 W. This means that the energy truly lost was of 133.6 W or 37.5% of the
input power. On the other hand, the chemical power used to convert limestone into lime was of almost
35 % of total power, adding the heating power as in equation (4.14), a total power of 167.4 W is used to
heat and convert the limestone, 47% of the input power, giving a thermal efficiency of 55.1 % (obtained
dividing the Pconversion by the absorbed power). In equation (4.14), the first term represents the integral
of the chemical heat source over the bed domain, it will be close to the theoretical value Pchem. A
revised energy balance is displayed in figure 4.20 where the energy used to raise the temperature is not
considered a loss.
Pconvertion =
∫bed
QChem dV + Pheat (4.14)
Figure 4.19: Energy balance of the limestone processing unit at steady state for a mass flow of 0.25kg/h.
The steady state data obtained with the given operational conditions (table 4.6) are given below in
table 4.8 where a summary of the major operational variables can be consulted. In figure 4.21 the
steady state distribution in a isoplane align with the zz axis for the temperature (a), loss factor (b),
57
Figure 4.20: Energy balance of the limestone processing unit at steady state for a mass flow of 0.25kg/h considering the Pheat as useful power.
microwave power deposition (c) and reaction heat source (d) are presented. From the displayed figures,
it is possible to visualize the interdependence of the four variables presented. For a higher temperature
there is a correspondent stronger loss factor, which will result in a hn higher microwave power deposition
at the same zone. Finally through figure 4.21 (d), one can attest how the reaction starts as soon as
temperature increases. It can be observed its evolution along the zz axis. Afterwards, the reaction rate
starts to decrease due to the lack of reactant.
Power input 356W
Material’s inlet temperature 293K
Max. bed temperature 1124K
Outlet mean bed temperature 583K
Outlet limestone mass fraction 0.7 %
plunger position 144mm
absorption efficiency 84.6 %
Bed power absorbed 301W
Convection losses 161W
Material’s outlet enthalpy 16W
Heating power to raise the material’s temperature 43.4W
Reaction power consumption 124W
Simulation time 13608 seconds
Table 4.8: Steady state data of the limestone processing unit.
Through figure 4.22 it is possible to visualize the electric field distribution (a), loss factor (b) and
microwave power deposition (c) from a top perspective (by defining a horizontal planar cut at roughly half
bed height normal to the xx axis). By analyzing the three images it is possible to notice the influence of
the electric field and the loss factor, two key variables of the Helmholtz equation (2.49), on the microwave
power deposition. It can be noticed how the power deposition manifests itself, in the both presence of
58
(a) Temperature distribution (K). (b) Loss factor.
(c) Total microwave power dissipation (W/m3) . (d) Heat source from the endothermic chemical re-action (W/m3).
Figure 4.21: Limestone processing steady state distributions (side view) of the temperature, loss factor,microwave power dissipation and the chemical reaction heat source.
a significant high electric field and high loss factor, as expected through equation (2.46). Hence it is
possible to attest that the microwave power dissipation field results from the intersection of the electric
field peaks with the loss factor ones (meaning high temperatures). Although the electric field plays an
important role in triggering the microwave heat source, its the loss factor that is the most crucial factor,
since its only peak is localized in a small zone. Further downstream the power deposition starts do
decay due to the absence of a strong electric field. A curious fact can be seen in the electromagnetic
field as two intense peaks are present.
(a) Electric field distribution(V/m).
(b) Loss factor. (c) Total microwave power dissi-pation (W/m3) .
Figure 4.22: Limestone processing steady state distributions (top view).
Regarding the Matlab controller, a remark should be made. The whole simulation discussed above
was conducted only with the autonomous intervention of the controller, once the initial conditions were
set. From the obtained results, it might be reasonable to consider that the approach taken to develop the
controller was a success. It was verified that the controller, by making an energy balance to the model
and accounting for the microwave efficiency, could cope with the evolution of the simulation and be able
to achieve a steady state condition. The particular moment corresponding to the first time interval (see
59
figure 4.14), can be considered note worthy. The controller was able to recover from a great efficiency
loss, due to an intentional low initial power input (that did not take into account the convective losses).
Regarding efficiency, it was noted that a 900 K initial temperature returned very high efficiency values
of roughly 97%. particularly when compared to the lowest efficiency obtained in the first time interval
(around 29%). This means that an high initial temperature, a sort of material pre-heating, can in fact
”kickstart” the process. And, when coupled with an adequate power, can reduce the required time to get
a steady state solution while always maintaining an high microwave efficiency.
Finally, it should be noticed the different variables used to develop de controller, that were defined
as probes in the COMSOL environment in order to return the required variables evolution. So that, the
power input and the optimum plunger position could be computed by equation 4.12 and the frequency
domain study. The particularity of the variables obtained through probes rely on the fact that they can
be related with the experimental apparatus, which means that the developed algorithm is not limited to
the numerical environment. For example, both the temperature at the metallic walls and of the material
at the outlet can be can be measured. Therefore, the convective power loss through the walls and
the enthalpy variation at the tube’s outlet can be estimated. So, by measuring the mass flow, one can
determine the amount of power required to convert all the material. Finally by measuring the reflected
microwave power, microwave efficiency can be found.
4.6.2 Mass flow parametric study
With the sole objective of understanding the impact of certain operational conditions on the developed
model, several simulations were conducted for different material’s mass flow while maintaining the same
material’s inlet temperature.
The steady state results for the limestone processing for a variety of different mass flows are dis-
played in table 4.9. The initial state for each mass flow simulation set was defined to be the steady state
of the previous. So, for a mass flow of 0.5 kg/h initial conditions were taken from the 0.25 kg/h mass flow
steady condition, for the 0.625 kg/h were taken from the 0.5 kg/h and so on. The aim of this approach
was to ensure a reduced simulation time, as it will strongly depend on the quality of the initial solution.
The last three entries of table 4.9 give information about the physical time required for each mass flow.
The time interval for each transient study was defined as approximately one quarter of the residence
time of each mass flow. In the entries ”g.” to ”m.” it is possible to find the power losses/usage the
respective impact in the energy balance. Entry ”k.” reflects the the ratio between the energy losses and
the absorbed power according to equation 4.15. It is possible to see that the true losses are computed
subtracting the heating enthalpy that was lost trough convection and did not leave at the tube’s outlet.
Entry ”m.” is the thermal efficiency for each mass flow. It is the ratio between the useful energy and
the absorbed power according to equation 4.16. The useful energy will be the energy consumed by the
reaction and the energy spent to heat the material to a suitable temperature (the considered 1073 K).
60
mass flow (Kg/h) 0.25 0.5 0.625 0.75 1
a. Power input (W) 356 573 684 793 1005b. Max. bed temperature (K) 1124 1156 1167 1171 1183c. Outlet mean bed temperature (K) 583 758 815 852 911d. Outlet limestone mass fraction (%) 0.7 0.4 0.7 1.2 1.1e. Plunger position (mm) 144 144 144 144 144f. Microwave absorption efficiency (%) 84.6 84.3 83.8 83.3 82.9g. Bed power absorbed (W) 301 483 573 661 833h. Convection losses (W) 161 185 193 198 208i. Material’s outlet enthalpy (W) 16 52 73 93 138j. Heating power to raise the material’s temperature (W) 43.4 86.78 108.47 130.16 173.55k. Losses (%) (eq: 4.15) 44.3 31.10 27.49 24.22 20.70l. Reaction power consumption (W) 124 247 309 370 489m. Thermal efficiency (%) (eq: 4.16) 55.6 69.72 72.86 75.67 79.54n. Total efficiency (%) 47.03 58.77 61.05 63.03 65.94o. Specific power (W/(Kg/h)) 1434 1151 1102 1070 1016p. Time interval for each study (s) 1512 756 600 504 372q. Number of required transient studies 9 7 7 7 7r. Total physical time of the simulations (s) 13608 5292 4200 3528 2604
Table 4.9: Parametric study results by variation of the mass flow rate.
Thermal efficiency% =Pheat +
∫bed
QChem dV
Asborbed power× 100 (4.16)
The specific power found in entry ”o.” is the power that was required to convert the tested mass flow
at the given conditions. It translates the ratio between the power input (entry ”a.”) and the converted
limestone mass flow (the converted mass flow was computed by subtracting the outlet mass fraction ”d.”
with the one from inlet that is equal to one).
From the gathered data of the steady state solutions, several remarks can be made. Regarding
the obtained temperatures, maximum bed temperature increases slightly over every mass flow and, as
expected, outlet temperature increases significantly, from the lowest (0.25 kg/h) to the highest (1 kg/h).
This behavior results from the increased axial speed, resulting in an hotter surface area and higher
convective losses. Microwave efficiency is showed to be quite similar over the range of simulated mass
flow rates. The entries ”k.” and ”m.” are the percentage of energy conveyed to the convective losses
and to convert the limestone, respectively. As can be noticed, there is a clear trend over the range of
mass flows. For a higher mass flow, the convection losses increase, however their weight decreases,
representing a lower percentage of the absorbed power. The behavior of useful power, used to heat
and convert the material, increases with the mass flow, but, this time, the thermal efficiency (eq: 4.16)
increases as well. Entry ”n.” displays the total efficiency for each mass flow, computed by multiplying
the microwave absorbed efficiency (entry f.) with the thermal efficiency (entry m.). The total efficiency
increases with mass flow, which was to be expected due to the increase in thermal efficiency for roughly
the same microwave absorption one. The discussed acknowledgment is reflected in the power input
61
required to convert one kilogram of limestone (entry ”o.”). As can be seen, for a higher mass flow, a
lower power input is enough to convert the same amount of mass when compared to a lower mass flow.
From the analysis to the parametric study it is possible to see that for a higher mass flow the total
efficiency increases while the specific power decreases. To obtain better conclusions about the impact
of mass flow in a limestone processing unit, it would be necessary to increase the mass flow. That would
have to be made until reach a point where it would be impossible to obtain a steady state solution, the
total efficiency would start to decrease or a temperature limit of the materials of the apparatus would be
violated.
In figure 4.23 the space distribution of the microwave power dissipation, temperature and chemical
heat source are displayed. The purpose of this figure is to serve as a supplement of the analysis of table
4.9 through a visual assist. The color range for the mass flows of 0.5 Kg/h and on are the same, so that,
the variations of each field could be easily noticed from one mass flow to another. As expected all three
field grow throughout the mass flow range. The microwave power dissipation increases due to the input
power due to the higher mass flow rate, which in turn, will produce a stronger electric field for the same
loss factor distribution. Although the loss factor is not represented, it peaks in the high temperature
zones, as so, it will be higher in the zones colored in dark red of the temperature field. As can be noticed
the power dissipation’s peak starts to develop in hotter areas, due to the higher loss factor.
Regarding the temperature, the dissipation is obtained when increasing the mass flow rate. With the
material being heated to the roughly the same temperature, combined with the faster travel time (less
residence time, so less convection time), temperatures will increase downstream, until the tube’s outlet.
The chemical reaction heat source increment happens because a higher mass flow means that more
material is required to be converted, and so, for each increasing mass flow an increasing part of the
power input is dedicated to this process. As can also be notice the temperature is the main responsible
for triggering the chemical heat source and, therefore, the chemical reaction.
62
(a) Microwave power dissipation(W/m3) for a mass flow of 0.25 kg/h.
(b) Temperature field (K) for a massflow of 0.25 kg/h.
(c) Chemical heat source (W/m3) fora mass flow of 0.25 kg/h.
(d) Microwave power dissipation(W/m3) for a mass flow of 0.5 kg/h.
(e) Temperature field (K) for a massflow of 0.5 kg/h.
(f) Chemical heat source (W/m3) for amass flow of 0.5 kg/h.
(g) Microwave power dissipation(W/m3) for a mass flow of 0.625 kg/h.
(h) Temperature field (K) for a massflow of 0.625 kg/h.
(i) Chemical heat source (W/m3) for amass flow of 0.625 kg/h.
(j) Microwave power dissipation(W/m3) for a mass flow of 0.75 kg/h.
(k) Temperature field (K) for a massflow of 0.75 kg/h.
(l) Chemical heat source (W/m3) for amass flow of 0.75 kg/h.
(m) Microwave power dissipation(W/m3) for a mass flow of 1 kg/h.
(n) Temperature field (K) for a massflow of 1 kg/h.
(o) Chemical heat source (W/m3) fora mass flow of 1 kg/h.
Figure 4.23: Converged solutions of the parametric study. 2D plots of the microwave power dissipation,temperature field and chemical endothermic heat source.
63
64
Chapter 5
Conclusions
This thesis is divided into two parts and presents an insight into the use of microwave energy as
an heating source in the formation of cement clinker. It enabled the understanding of the impact of key
operational parameters in microwave heating and the development of an efficient microwave limestone
processing unit.
In the first part the chemical mechanism and the behavior of microwave induced plasma were ad-
dressed. Two models were built, respectively in order to reenact related literature data. The results
obtained turn out to be a mild success. The chemical model was able to predict the evolution of the
complete cement clinker chemical process with reasonable results, being validated with the available
data in the literature. Regarding plasma, the developed model strafed way from the intended purpose,
nevertheless, it was able to capture the typical behavior of a microwave induced plasma. In all, both mod-
els contributed to the general understanding of the involved processes and were reasonable enough to
prove that the software used, COMSOL, was able to handle with such challenges.
On the second part, a 3D microwave heating model was developed for converting a key component
in cement clinker, limestone. 3D transient simulations were carried resorting to COMSOL and controlled
by a code developed in a MATLAB environment. This simulation coupled the three involved physics. The
chemical and thermal fields are coupled through the Arrhenius equation used to compute the reaction
rate. The electromagnetic and thermal fields are coupled through the dielectric properties of temperature
and the resulting feedback dependency of the heating source.
By controlling the cavity geometry, and hence, the resonance of the electromagnetic field, and con-
trolling the microwave power input, the model was able to attain a steady state with an optimized mi-
crowave efficiency and power usage. It is rather clear how the interception of the the electromagnetic
field and the loss factor spatial distribution results in the much needed microwave power dissipation,
which triggers both the heating and chemical processes. Therefore, it was showed the importance of
a correct electric field placing (through varying the plunger position) and maintaining a high material
temperature in the cavity (matching an high loss factor) in order to achieve optimum conditions for lime-
stone processing. From the conducted parametric study, it was possible to observe a tendency where an
higher mass flow returns a lower specific power input required to convert the same amount of limestone.
65
5.1 Achievements
Considering all the carried simulations it is quite safe to conclude that COMSOL is a suitable tool to
tackle a variety of multiphysics problems. The MATLAB controller was a proven success, as it conducted
the transient simulation with the necessary adjustments without any user intervention during the con-
verging process. Thus, enabling to achieve an optimized and efficient microwave limestone processing
model, while avoiding temperature related problems, by adjusting operational parameters such as the
plunger position and input microwave power. Moreover, and unlike other models published in the litera-
ture, the proposed controller is also able to guarantee total conversion of the chemical reactant. Finally,
it was showed that the developed controller could be applied outside of the numerical simulation, as all
the data used by it can be also be measured in an experimental apparatus.
5.2 Future Work
Considering the continuation of this work, there is plenty of ways to improve the accuracy and better
portray the reality of limestone or cement clinker processing. Although increasing the complexity, some
steps/mechanisms can be added to the model. Variations in bed height and density shall be accounted
for due to the gaseous chemical products (CO2 for limestone calcination) that flow out of the bulk ma-
terial. A diffusion model can be coupled to better depict the gaseous phase. The pseudo-fluid behavior
assumed for the bed material can be changed for particles and small bulks of material, which, through
the use of a discrete element method, can better portray the movement of the chunks of material along
the rotating tube, describing the real behavior of the material inside the cavity. This would increase the
importance of the cavity geometry adjustments, as the temperature field would be far more dynamic.
Finally the controller can be used to study the design of new cavities and controllers.
66
Bibliography
[1] A. Buttress, A. Jones, and S. Kingman. Microwave processing of cement and concrete materials –
towards an industrial reality ? Cement and Concrete Research, 68:112–123, 2015.
[2] J. H. Potgieter. An overview of cement production : How “ green ” and sustainable is the industry?
Environmental Management and Sustainable Development, 1(2):14–37, 2012.
[3] N. Makul, P. Rattanadecho, and D. K. Agrawal. Applications of microwave energy in cement and
concrete – A review. Renewable and Sustainable Energy Reviews, 37:715–733, 2014.
[4] D. E. Clark and W. H. Sutton. Microwave processing of materials. Annual Review of Materials
Science, 26:229–231, 1996.
[5] C. M. Hansson. Concrete : The advanced industrial material of the 21st Century. Metallurgical &
Materials Transactions A, 26:1321–1341, 1995.
[6] F. A. Joekes and I. Rodrigues. Cement industry: sustainability, challenges and perspectives. Envi-
ronmental Chemistry Letter, pages 151–166, 2011.
[7] P. Rattanadecho, N. Suwannapum, B. Chatveera, D. Atong, and N. Makul. Development of com-
pressive strength of cement paste under accelerated curing by using a continuous microwave ther-
mal processor. Materials Science and Engineering A, 472(1-2):299–307, 2008.
[8] X. Wu, J. R. Thomas, W. A. Davis, X. Wu, J. R. Thomas, and W. A. Davis. Control of thermal
runaway in microwave resonant cavities. Journal of Applied Physics, 92(6), 2002.
[9] L. Quemeneur, J. Choisnet, and B. Raveau. Les micro-ondes peuvent-elles etre utilisees pour la
clinkerisation de crus des cimenterie? Material Chemistry Physics, 8:293–303, 1983.
[10] A. A. Salema and M. T. Afzal. Numerical simulation of heating behaviour in biomass bed and pellets
under multimode microwave system. International Journal of Thermal Sciences, 91:12–24, 2015.
[11] R. M. C. Mimoso, D. M. S. Albuquerque, J. M. C. Pereira, and J. C. F. Pereira. Simulation and con-
trol of continous glass melting by microwave heating in a single-mode cavity with energy effiiency
optimization. International Journal of Thermal Sciences, 111, 2017.
[12] A. P. Watkinson and J. K. Brimacombe. Limestone calcination in a rotary kiln. Metallurgical Trans-
actions B, 13B:369–378, 1982.
67
[13] K. S. Mujumdar, A. Arora, and V. V. Ranade. Modeling of rotary cement kilns : applications to re-
duction in energy consumption. Industrial Engineering Chemistry Research, 45:2315–2330, 2006.
[14] H. A. Spang. A dynamic model of a cement kiln. Automatica, 8(3):309–323, 1972.
[15] E. Mastorakos, A. Massias, C. D. Tsakiroglou, D. A. Goussis, V. N. Burganos, and A. C. Payatakes.
CFD predictions for cement kilns including flame modelling, heat transfer and clinker chemistry.