Article pubs.acs.org/IECR
Energy-Efficient Novel Heterogeneous Gaseous T‑Junction Microreactor Design Utilizing Inlet Flow Pulsation Balaji Mohan,† Jiang Puqing,† Agus P. Sasmito,*,‡ Jundika C. Kurnia,†,∥ Sachin V. Jangam,§ and Arun S. Mujumdar‡,⊥ †
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576 Department of Mining and Materials Engineering, McGill University, 3450 University St., Adams Bldg, Room 115, Montreal, Quebec, Canada H3A 2A7 § Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore, 117585 ∥ Mechanical Engineering, Masdar Institute of Science and Technology, Masdar City, P.O. Box 54224, Abu Dhabi, United Arab Emirates ⊥ Department of Chemical and Biochemical Engineering, University of Western Ontario, London, Ontario, Canada N6A 3K7 ‡
ABSTRACT: The objective of the study is to investigate the effects of inlet flow pulsation on the mixing and reaction performance of a heterogeneous gaseous T-junction microreactor numerically. The idea is to have a novel modular microreactor design comprised of two microreactors (A and B), arranged in parallel, and a valve to control the flow direction. Flow pulsation can then be implemented to alternately supply reactant to microreactor A and microreactor B. Hence, by feeding the same amount of reactant and thus same pumping power/parasitic loads, the new design is able to run two microreactors and could achieve almost the same level of performance as that of a steady flow microreactor with an expense of one microreactor. The study was carried out for a case of mixing and heterogeneous catalytic reaction of methane (gaseous fuel) oxidation at the microreactor surface coated with a platinum catalyst. A detailed parametric study was performed to include the effect of frequency, amplitude, phase difference, and different waveforms on the conversion rate of gaseous fuel and pressure drop across the microreactor. The results suggest that the flow pulsation marginally affects the reaction performance, in which, the whole novel modular system produces almost double yields and energy (temperature) than that of conventional steady flow single microreactor design under the same amount of inlet reactants. This highlights the potential of this novel design in saving energy, enhancing reactants utilization, and increasing yield production for several applications.
1. INTRODUCTION Microreactors and micromixers have been receiving significant attention especially in the chemical industries. The term “microreactors” refers to systems with characteristic length scales that are in the micrometer range. The potential advantages of using microreactors over conventional reactors include portability, safety, and better control of reaction conditions. According to Brody et al.,1 the tangible effect of this small dimension is that transport processes become increasingly controlled by viscous forces rather than inertia. On the other hand, the reduced dimensions of the microreactor system lead to a large surface-to-volume ratio, which increases heat and mass transfer efficiency. Micromixers can be divided broadly into passive and active micromixers. Passive micromixers rely on diffusion or chaotic advection, while active micromixers rely on external disturbances. T-junction micromixer is one of the most commonly used passive micromixer. Extensive experimental and numerical investigations2−9 on mixing processes in T-junction micromixers have been conducted and reported. Typically, a long channel is necessary to achieve desired mixing for a T-junction microchannel. In order to enhance mixing, various approaches such as addition of fins and application of coiled tubes have been proposed and evaluated. Those designs, however, impose higher pressure drop and manufacturing difficulties compared © 2014 American Chemical Society
to straight T-junction designs. Thus, there is a demand for improvement in mixing process in straight T-junction design. Flow pulsations have been shown to enhance heat and mass transfer in macroreactors. Hence, it is of interest to confirm whether it is also suitable to improve the mixing process in microreactors. Karamercan and Gainer10 studied the effect of pulsations on heat transfer and found that the heat-transfer coefficient increases with the pulsations, with the highest enhancement being observed in the transition flow regimes. Honaker and Tao11 studied the effect of sonic pulsations on the mass-transfer rate of naphthalene from a plate to air and found that, within the useful sonic pulsation ranges of amplitude and frequency, the local mass-transfer rate is affected by the fluctuating components of velocity, concentration, and time-averaged gradient of air velocity at the interface. Abiev has studied the effect of oscillation frequency in the extraction process and found that there exist an optimum range of frequency for liquid extraction of a desired substance from the particle.12,13 Special Issue: Ganapati D. Yadav Festschrift Received: Revised: Accepted: Published: 18699
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Figure 1. Schematic of proposed new modular microreactor design.
Zohir et al.14 studied the effect of heat transfer by introducing pulsation and found that the heat-transfer rate was enhanced by 50% at a Reynolds number of Re = 8000 for large-diameter (50 mm) tubes but was reduced up to 35% for smaller-diameter (15 mm) tubes for the same Reynolds number. Zaki et al.15 found that the pulsating flow enhanced mass transfer by a factor of 1.2−5.5, compared to the steady laminar flow value. Xu et al.16 proved a significant enhancement of heat transfer by 18.6% for heating and 19.1% for cooling at the target surface by the intermittent pulsation in a turbulent impinging jet by simulation results. Akdag17 studied the forced convection heat transfer around a discrete heater located in a channel subjected to laminar pulsating airflow numerically and found that thermal transport from the heater is greatly affected by the frequency and amplitude of the flow pulsation. It was found that the heat transfer was enhanced by 25% for high amplitude and low frequency. Available literature shows that the heat- and mass-transfer rates can be enhanced by flow pulsation. Here, we propose a novel idea of introducing pulsating inflow in a heterogeneous gaseous T-junction microreactor. The proposed inlet flow pulsation offers possibility for energy savings, reactant utilization enhancement, and production rate improvement. The idea is to have a new modular microreactor design that is comprised of two microreactors (A and B) arranged in parallel and a valve to control the flow direction, as shown in Figure 1. Flow pulsation can then be applied to dynamically alternate the supply of reactants to microreactor A and microreactor B. While this configuration is promising, one aspect remains questionable: how significant is the effect of inlet flow pulsation to the reaction? Therefore, the objective of the study presented herein is 2-fold:
(i) To investigate effect of key operating pulsation parametersfrequency, amplitude, phase difference, and waveformwith regard to the reaction performance; and (ii) To evaluate the feasibility of inlet flow pulsation to the proposed modular microreactor design. Therefore, we would like to quantify the effect of inlet pulsation to the reaction performance. By feeding the same amount of reactant and thus same pumping power/parasitic loads, the new design would be able to operate two microreactors and could achieve almost the same level of performance as that of the steady-flow microreactor with an expense of one microreactor. For instance, if this is the case, the overall efficiency of the system would increase around twice than that of a steady-flow single microreactor. The layout of the paper is as follows. First a mathematical model was developed with governing conservation equations of mass, momentum, energy and species and was solved using CFD solver. Then the effect of inflow pulsation was evaluated in terms of outlet temperature, pressure drop and conversion rate defined later. Finally conclusions are drawn based on the results obtained.
2. MATHEMATICAL MODEL The physical model used in the simulation is a two-dimensional T-junction microchannel, as shown in Figure 2. The dimensions of the T-junction are L = 120 mm and W = 1 mm. Air enters the T-junction microchannel from one wing (green arrow in Figure 2), while gaseous fuel enters from the other (red arrow in Figure 2). The gaseous fuel is methane. Both air and gaseous fuel are made to enter the microchannel with pulsating velocities. The interior walls of the microchannel, just after the junction point are coated with platinum, 18700
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Article in T = Tair ,
ωO2 = ωOin2 ,
ω N2 = 1 − ωOin2
(7)
• Fuel inlet: The gaseous fuel flow is introduced with pulsating flow under the following conditions For sine wave: in u = Ufuel +
A sin(2πft + φfuel) 2
(8)
For square wave: in + u = Ufuel
in T = Tfuel ,
4 π
∞
∑ l=1
A sin((2k − 1)2πft + φfuel) 2 (2k − 1)
in ωCH4 = ωCH , 4
in ωH2 = 1 − ωCH 4
(9) (10)
• Outlet: The outlet refers to the pressure outlet under the following conditions: P = Pout ,
u = 0,
which acts as the catalyst for the well-known combustion reaction between methane and air. The flow is considered to be unsteady and Newtonian flow. Both air and gaseous fuel are miscible and follow the ideal gas law. 2.1. Governing Equations. The conservation equations of mass, momentum, species, and energy18 are
{ }
∂ρCpT ∂t
+ ∇·(ρCpT u) = ∇·(ke∇T ) + Stemp
u = 0,
(2)
(3)
Ng
∞
∑ k=1
A sin((2k − 1)2πft + φair) 2 (2k − 1)
T = Twall
(13)
Nb
Ns
∑ gi′,r Gi + ∑ bi′,r Bi + ∑ si′,rSi i=1
i=1 κr
Ng i=1
i=1 Nb
⇄ ∑ gi″, r Gi +
Ns
∑ bi″, r Bi +
∑ si″, rSi
i=1
i=1
(14)
where Gi represents the gas-phase species, Bi represents the solid species, and Si represents the surface-adsorbed species, respectively. The parameters g′, b′, s′ are the stoichiometric coefficients for each reactant species, and g″, b″, and s″ are stoichiometric coefficients for each product species. κr is the overall reaction rate constant. Since only the species involved as reactants or products will have a nonzero stoichiometric coefficient, the rate of reaction is calculated as
For square wave: 4 π
(12)
2.3. Chemical Reactions. The chemical reaction involved in the current simulation is mainly catalytic oxidation of methane on the inner wall of the channel, which is coated with a thin layer of platinum catalyst. Note that this reaction is chosen as an example of heterogeneous gaseous reaction model; other type of reaction can be easily implemented within the framework derived here. Species involved include 7 gas species (CH4, O2, H2, H2O, CO, CO2, and N2), 11 surface species (H(s), Pt(s), O(s), OH(s), H2O(s), CH3(s), CH2(s), CH(s), C(s), CO(s), CO2(s)) and one bulk/solid species (Pt(b)), which describe the coverage of the surface with adsorbed species that are included in the model. The detailed multistep reaction mechanism and its reaction rate constants are listed in Table 1. The gas-phase species and surface species can be produced and depleted by surface reaction; hence, it is written in a general form as
∂(ρωi) + ∇·(ρ uωi) = ∇·(ρDi∇ωi) + R i (4) ∂t where ρ is the fluid density, u the fluid velocity, p the pressure, μ the dynamic viscosity, T is the temperature, CP is the specific heat capacity of the fluid, ke the effective thermal conductivity, Stemp the heat release or absorb due to the reaction, ωi the mass fraction species i, Di the diffusion coefficient of species i, Ri the mass produced or consumed by the reactions. 2.2. Boundary Conditions. The boundary conditions for the flow through a microchannel T-junction are as follows: • Air inlet: The oxidant flow is introduced with a pulsating flow under the following conditions: For sine wave: A in u = Uair + sin(2πft + φair) (5) 2
in + u = Uair
n ·∇T = n ·∇ωi = 0
• Reacting walls: At the interior channel walls after the Tjunction, surface reaction is taken into account and it is considered to have no-slip conditions with a constant wall temperature
(1)
∂ρ u + ∇·ρ uu = −∇pI + ∇· [μ(∇u + (∇u)T )] ∂t 2 + μ(∇·u)I 3
(11)
• Nonreacting walls: The nonreacting walls are specified as no-slip conditions, no species flux, and adiabatic at the channel wall before the T-junction:
Figure 2. Schematic representation of the microchannel T-junction examined.
∂ρ + ∇·ρ u = 0 ∂t
n ·∇(u ·ey) = n ·∇T = n ·∇ωi = 0
(6) 18701
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Table 1. Surface Reaction Mechanism reaction
1 2 3 4 5 6 7 8 9 10
H2 + 2Pt(s) → 2H(s) 2H(s) → H2 + 2Pt(s) O2 + 2Pt(s) → 2O(s) O2 + 2PT(s) → 2O(s) 2O(s) → O2 + 2Pt(s) H2O + Pt(s) → H2O(s) H2O(s) → H2O + Pt(s) OH + Pt(s) → OH(s) OH(s) → OH + Pt(s) H(s) + O(s) → OH(s) + Pt(s) H(s) + OH(s) → H2O(s) + Pt(s) OH(s) + OH(s) → H2O(s) + O(s) CO + Pt(s) → CO(s) CO(s) → CO + Pt(s) CO2(s) → CO2 + Pt(s) CO(s) + O(s) → CO2(s) + Pt(s) CH4 + 2Pt(s) → CH3(s) + H(s) CH3(s) + Pt(s) → CH2(s) + H(s) CH2(s) + Pt(s) => CH(s) + H(s) CH(s) + Pt(s) → C(s) + H(s) C(s) + O(s) → CO(s) + Pt(s) CO(s) + Pt(s) → C(s) + O(s) OH(s) + Pt(s) → H(s) + O(s) H2O(s) + Pt(s) → H(s) + OH(s) H2O(s) + O(s) → OH(s) + OH(s)
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Ng
βr
Ar
No.
g′
4.36 3.7 1.8 2.01 3.7 2.37 1 3.25 1 3.7
× × × × × × × × × ×
107 1020 1017 1014 1020 108 1013 108 1013 1020
0.5 0 −0.5 0.5 0 0.5 0 0.5 0 0
Er (J/kmol) 0 6.74 × 0 0 2.13 × 0 4.03 × 0 1.93 × 1.15 ×
10
∂[Si]wall = R̂ i ,site ∂t
8
108 107
1.74 × 107
3.7 × 1020
0
4.82 × 107
1015 1013 1013 1020
0.5 0 0 0
0 1.25 × 108 2.05 × 107 1.05 × 108
2.3 × 1016
0.5
0
3.7 × 1020
0
2 × 107
3.7 × 1020
0
2 × 107
3.7 × 1020
0
2 × 107
3.7 × 1020
0
6.28 × 107
1 × 1017
0
1.84 × 108
1.56 × 1018
0
1.15 × 107
1.88 × 1018
0
1.74 × 107
4.45 × 1020
0
4.82 × 107
while ṁ dep is the net rate of mass deposition or etching as a result of surface reaction, given by Nb
[Si]wall is the site species concentration at the wall, and this parameter is defined as [Si]wall = ρsite zi
M= −1 ⎛ ωCH ωH2 ωO2 ωH2O ωCO2 ω N2 ⎞ ωCO 4 ⎜⎜ ⎟ + + + + + + M H2 MO2 M H2O MCO2 MCO M N2 ⎟⎠ ⎝ MCH4
The gas mixture viscosity, μ,17 is defined as xαμα μ=∑ α ∑β xβφα , β with α , β = CH4 , H 2 , O2 , H 2O, CO, CO2 , N2
where xα, xβ are the mole fractions
i = 1, 2, 3 , ..., Ng φα , β
Nrxn
i = 1, 2, 3 , ..., Nb
i = 1, 2, 3 , ..., Ns (16)
of species α and β
2 −1/2 ⎡ ⎛ (g ) ⎞1/2 ⎛ M ⎞1/4 ⎤ μ ⎢ ⎥ Mα ⎞ 1 ⎛ β ⎜ α ⎟ ⎜⎜1 + ⎟⎟ = ⎟ ⎥ ⎢1 + ⎜ (g ) ⎟ ⎜ 8⎝ Mβ ⎠ ⎝ μβ ⎠ ⎝ Mα ⎠ ⎥⎦ ⎢⎣
ke =
∑ kiωi i
while the reaction rate constant is computed using the Arrhenius expression, which is given by kf ,r
(25)
The multicomponent gas mixture thermal conductivity (ke) is defined by
Nrxn
⎛ E ⎞ = A r T βr exp⎜ − r ⎟ ⎝ RT ⎠
19
(26)
r=1
r=1
(23)
where R is the universal gas constant and M denotes the mixture molecular weight, given by
r=1
∑ (si″,r − si′,r)ℜr
pM RT
ρ=
Nrxn
R̂ i ,site =
(22)
where ρsite is the site density of the catalyst and zi is the site coverage of species i. 2.4. Constitutive Relations. The gas density is given by the ideal gas law:
where [Gi]wall represents the molar concentration on the wall. Thus, the net molar rate of production or consumption of each species i is given by
∑ (bi″,r − bi′,r )ℜr
(21)
i=1
(15)
i=1
R̂ i ,bulk =
∑ Mω ,iR̂ i ,bulk
ṁ dep =
s′
∑ (gi″,r − gi′,r )ℜr
(19)
(24)
i ,r i ,r ℜr = k f , r ∏ [Gi]wall [Si]wall
R̂ i ,gas =
i = 1, 2, 3 , ..., Ns
The gas concentration at the wall is calculated from the species mass fraction, which is defined as ρ ωi ,wall [Gi]wall = wall Mω , i (20)
107
0
× × × ×
(18)
107
3.7 × 1020
7.85 1 1 3.7
∂ωi ,wall
− ṁ depωi ,wall = Mω , iR̂ i ,gas ∂n i = 1, 2, 3 , ..., Ng
ρwall Di
(27)
while the gas-mixture specific heat capacity (Cp) is evaluated using Cp =
(17)
On the reacting wall surface, it is assumed that the mass flux of each gas species is balanced with its rate of production/ consumption; this is given by
∑ ωiCp,i i
(28)
The results are later discussed in terms of conversion rate. The conversion ratio is used to evaluate the effectiveness of the 18702
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Figure 3. Validation with experimental data at low and high inlet stoichiometry.
velocities, mass fractions, pressure and temperatures pulsating with time were monitored as the calculation carries on. 2.6. Validation. The validation of any mathematical model involving mixing and reactions is very important, recalling its complexity of coupled physical phenomena and interaction between species and its chemical kinetics. The mathematical model used in this simulation is validated against the experimental results of Bond et al.20 and model prediction by Canu.21 The methane conversion rate in monolithic reactor was approximated as a repeating single channel flow; see Bond et al.20 for details of the experimental setup. The validation is initiated with methane catalytic oxidation at a low stoichiometry gas inlet (ξ = 0.18); after which the methane conversion rate of higher inlet stoichiometry (ξ = 0.39) is compared, as depicted in Figure 3. It is found that the model predictions agree well with the methane conversion rate from experimental counterpart at both low and high inlet stoichiometry. In addition, the model has better agreement as compared to model prediction by Bond et al.20 and Canu21 especially at high methane stoichiometry. This implies that the model correctly accounts for the fundamental physics associated with the reactions. The validated mathematical model is then extended to account for transient operation with inlet flow pulsation. It is expected that adding transient term to the governing equations does not affect the validity of the models since it is derived from the first principle accounting for transient transport phenomena. While experimental evidence and validation for a corresponding inlet flow pulsation would be ideal, lack of such evidence does not limit this study as the phenomena observed experimentally are well captured in the present model. In addition, the steady-state reaction results provide the baseline for comparison with the transient pulsation operation. Comparison against transient response of an inlet flow pulsation from experiments will be considered in future study to further improve the validity of its prediction.
mixing and reaction rate in the microchannel. The conversion rate of methane (η) is defined as ω − ωout η = in ωin (29) where ωin is the mass fraction of methane at the junction and ωout is the mass fractions of methane at the outlet. The mass flow rate of methane, ṁ CH4, is calculated by
ṁ CH4 = CmolVAMCH4
(30)
where Cmol is the molar concentration of methane, which can be exported from FLUENT directly, V is the bulk velocity, A is the channel’s cross-sectional area, and MCH4 is the molar mass of methane. The mass fraction then is calculated from the mass flow rate of methane and the total mass flow rate (ṁ tot) as ωCH4 =
ṁ CH4 ṁ tot
(31)
2.5. Numerical Approach. The model geometry was meshed with GAMBIT, which is preprocessor software of the FLUENT package. Three different number of elements2.5 × 105, 5 × 105, and 1 × 106were used in this study to compare the local pressure, velocities, species mass fractions, and temperatures to ensure a mesh-independent solution. It was found that the mesh size of 5 × 105 gave ∼1% deviation, compared to a finer mesh size of 1 × 106; whereas the results from the mesh size of 2.5 × 105 gave ∼10% deviation, compared to those from the finest mesh design. Therefore, a mesh consisting of ∼5 × 105 elements was found to be sufficient for the numerical experiments for our study. A fine structured mesh was used near the wall to resolve the boundary layer and an increasingly coarser mesh was implemented in the middle of the channel to reduce the computational cost. A segregated time-dependent unsteady solver in FLUENT 6.3.26 was used for the calculation. Gas properties and reaction mechanisms were defined using CHEMKIN software and userdefined functions (UDFs) were written in C language to account for the temperature-dependent thermophysical properties of the fluids used in the study. UDFs were written in C language to provide the pulsating inlet velocities. Data of
3. RESULTS AND DISCUSSION Numerical simulations were carried out to study the effect of inlet pulsation frequency, amplitude and phase difference on the microreactor performance. For each group of simulation, 18703
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outlet temperature and conversion rate are calculated as timeaveraged parameters over a time period. The averaged values are shown in Table 3. In addition, the amplitude or average values of outlet bulk temperature and conversion rate of methane are marginally affected by different frequencies. Considering that the channel length is only 20 mm and the average velocity of fluid is 5 m/s, ∼0.004 s is needed for the fluid to completely flow through the channel. For the cases in Figure 4, the inlet pulsation frequency is probably too low so that, during the interval of 0.004 s, the inlet velocity changes are too small to notably affect the performance. A new group of cases were then studied; with the inlet pulsation frequency increased to 30 Hz, 70 Hz, 100 Hz, 200 Hz, and 1 kHz, while the peak amplitude is kept constant at 0.5 m/ s, as shown in Figure 5. Note that it might not be practically possible to achieve a high frequency of 1 kHz in real systems right now; however, this might be feasible on future application with the advancement of microtechnologies. Figure 5 shows that the averaged results of pulsating cases with increased frequencies do not vary significantly from those of the base case; however, their pulsating peak amplitudes vary considerably, especially for the case of 1 kHz. The maximum peak amplitude was found at frequency of 70 Hz and when the frequency was increased the peak amplitude decreased. The increased amplitude of temperature reaches maximum at 70 Hz frequency, which may be due to average residence time at this frequency being proportional to the quarter of pulsation period, i.e., T/4 = (1/4)f.12 When the frequency is further increased to 1 kHz, the outlet temperature is more stabilized while the pressure drop and methane conversion rate pulsate at larger peak amplitudes. Comparison also shows there is a phase shift of outlet temperature and pressure drop relative to the inlet pulsation rate when the inlet frequency is increased. It thus can be inferred that the outlet temperature can be stabilized either by decreasing the frequency to zero, or by increasing it to an extremely high value, albeit the maximum peak of the outlet temperature can be found if the average residence time is proportional to the quarter of pulsation period, i.e., T/4 = 1/4f, for which in this particular case is at the frequency 70 Hz. This can be explained by the fact that, as we look closer to the fine characteristic of flow, inlet pulsation creates oscillating flow which leads to dynamics velocity profiles (at some point the flow become not fully developed) and higher convective and diffusive transport, which, in turn, is translated to a higher reaction rate. Figure 6 shows that for the first two cases (100 and 200 Hz), the inlet and outlet total mass flow rate pulsate at the same amplitude and the same frequency, with a slight phase lag that the outlet mass flow rate is behind the inlet. This result is reasonable that by the law of mass conservation the outlet mass flow rate should be the same with the inlet; and since it takes time for the fluid to flow through the channel the outlet flow rate should lag behind the inlet. For the case of 1 kHz, however, the outlet mass flow rate pulsates at smaller amplitude than the inlet, totally different from the previous cases. This is probably due to the fact that at very high frequency, i.e., 1 kHz, the gasdynamics of pulsation flow is much faster than the dynamics of reaction rate, thus there is a delay on the reaction process which leads to difference between the inlet and outlet mass flow rate. Further experimental confirmation is required to clarify this hypothesis. 3.2. Effect of Pulsation Amplitude. Cases with same pulsation frequency (100 Hz) but different peak amplitudes (2
either two of the three parameters were set constant to study the effect of other parameter. For all cases, the average inlet velocity was set as 5 m/s, corresponding to an inlet Reynolds number of ∼300. Simulation results show that the highest velocity occurs at the outlet, and is ∼24 m/s, corresponding to a Reynolds number of 1400. This provides firm indication that the flow in the channel is laminar. A base case was studied for comparison reasons. The physical and geometrical parameters, along with the properties of fluids used in the simulations, are listed in Table 2. This base case has Table 2. Parameters and Properties Used in Simulations parameter
value/comment
length, L width, W Pout Pt(S) Tinair, .Tinfuel. Twall Uinair, Uinfuel ωinO2
120 × 10−3 m 1 × 10−3 m 101325 Pa 2.7063 × 10−8 kg mol m−2 300 K 1290 K 5 m s−1 0.21
ωinCH4
0.9
μair μCH4
1.7894 × 10−5 kg m−1 s−1 1.0295 × 10−5 kg m−1 s−1
ρair ρCH4
1.1839 kg m−3 0.6797 kg m−3
identical time-dependent setup as other cases. The only different is that the inlet velocities are set constant at 5 m/s. Results of the base case are compared with all the other pulsating cases in the following analysis. If not stated otherwise specifically, the horizontal lines in the following graphs are values of the base case. 3.1. Effect of Frequency. Cases with the similar average velocity and peak amplitude but different pulsation frequencies were examined to study the effect of inlet pulsation frequency on micromixer performance. Figure 4 shows the results of cases with an average velocity of 5 m/s and a peak amplitude of 2 m/ s but the pulsation frequency varies at 0.2 Hz, 0.5, and 10 Hz, respectively. Comparison of these cases indicates that the outlet bulk temperature and methane conversion rate pulsate at the same frequencies corresponding to the inlet velocity frequency. Figure 4 also shows that, when the inlet velocities of methane and air increase, the conversion rate of methane also increases while the outlet temperature decreases, and vice versa. It should be noted that the molar proportion of methane and oxygen is constant as long as their inlet velocities are at constant ratio. The increased conversion rate of methane corresponding to increased inlet velocity can be explained by the fact that the increase in inlet velocity triggers faster product removal, thus increasing the possibility of the mixture of fuel and oxygen to come into contact with the wall and react. In addition, the chemical reaction of methane oxidation is exothermic; the decreased outlet temperature corresponding to increased inlet velocity indicates that the bulk fluid temperature is mainly heated by the wall instead of by heat generation from the chemical reaction. Comparison of pulsating cases with the base case shows that pulsating cases have marginally higher average outlet temperature and lower average methane conversion rate. The averaged 18704
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Figure 4. Effects of frequency on outlet bulk temperature and methane conversion rate (frequency = 0.2, 0.5, and 10 Hz).
Table 3. Averaged Outlet Temperature and Conversion Rate Frequency average outlet temperature average conversion rate
Amplitude
base case
0.2 Hz
0.5 Hz
10 Hz
30 Hz
70 Hz
100 Hz
200 Hz
1 kHz
2 m/s
0.5 m/s
725 0.093
750 0.088
750 0.088
750 0.088
725 0.093
725 0.093
725 0.093
725 0.093
725 0.093
725 0.093
725 0.093
and 0.5 m/s) were studied to investigate the effect of pulsation amplitude on microreactor performance. Figure 7 shows the comparison between different amplitudes. Comparison shows that the averaged values of outlet temperature, pressure drop, and methane conversion rate are the same, but they pulsate at higher amplitudes when the inlet velocity pulsates at higher amplitude. Thus, it is concluded that the pulsation amplitude of inlet velocity does not have particular effect in enhancing methane conversion rate or
decreasing average pressure drop; the smaller the pulsation amplitudes of inlet velocity, the more stable the performance. 3.3. Effect of Phase Difference. The effect of phase difference between air and fuel inlet in terms of π/4, π/2, 3π/4, and π were studied in comparison with the base case. The peak amplitude (0.5 m/s) and frequency (1 kHz) of the flow are kept constant in this study. Figure 8a shows the inlet velocity of air and gaseous fuel for different phase differences with flow time. 18705
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Figure 5. Effects of high frequency on outlet bulk temperature, pressure drop, and methane conversion rate.
Figure 8b shows the conversion rate over flow time pulsates with different amplitudes from the base conversion rate though
the time averaged conversion rate remains same for all the cases. It was also found that the amplitude of conversion rate 18706
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Figure 6. Inlet and outlet mass flow rate with different frequencies (a) 100 Hz, (b) 200 Hz, and (c) 1 kHz).
Figure 7. Effect of pulsation amplitude on outlet temperature, pressure drop, and methane conversion rate. (Peak amplitude = 2 m/s, 0.5 m/s.)
decreases as phase difference increases and then for a phase difference of π it again increases. As the phase difference is introduced, the air enters the channel prior to the methane; thus, it has time to reach the optimum temperature for the
reaction to occur by heat transfer through convection from the walls, which reduces the chemical and ignition lag between them. The temperature of air increases as the phase difference increases due to a longer time for temperature rise to occur. For 18707
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Figure 8. (a) Inlet velocity profile, (b) methane conversion rate, and (c) pressure drop with phase difference.
Figure 9. Comparison of inlet velocity, outlet temperature, pressure drop, and conversion rate of different waveforms.
phase difference of π, although air gets maximum time for temperature rise, the high-temperature air leaves the channel before the fuel enters the channel as the half time period selected for the study is lesser than the time taken for the flow to leave the channel thus the amplitude of conversion rate
increases. In addition, phase difference allows for species to have sufficient time to transport; however, for this fast reaction, it hinders the reaction from occurring simultaneously and results in a decrease in the outlet amplitude. 18708
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mass transport phenomena in a T-junction microreactor. It was found that • By introducing inlet pulsation, the average outlet temperature becomes slightly higher while the methane conversion rate becomes slightly lower. • The average value of pressure drop or methane conversion rate is marginally affected by the frequency or peak amplitudes of inlet pulsation. • The pulsation amplitudes of outlet bulk temperature and methane conversion rate are not significantly affected when it is lower than 1 kHz; however, when the frequency is larger than 1 kHz, the heat-transfer rate tends to have less fluctuations and, therefore, is more stable. • For much smaller amplitudes, a more stable performance can be achieved. • When there is a phase difference between the inflow pulsations, it was found that phase difference of 3π/4 with fuel lagging behind air gave a more stable performance; but considering the pressure drop, the phase difference of π is the most stable. • Upon studying the effect of different waveforms, it is found that sine wave pulsations are more stable in terms of performance than square wave pulsations. The computational results indicate that the inflow pulsations have a marginal effect on augmenting reactor performance (in terms of conversion rate and temperature profile). Recalling our proposed modular microreactor design, however, these results suggest that the entire system (comprising two parallel microreactors) produce almost double yields and energy (temperature) than that of conventional steady flow single microreactor design under the same amount of inlet reactants. This highlights the potential of this new design in saving energy, enhancing reactants utilization and increasing yield production for several applications: microcombustion, chemical processes, pharmaceutical and other applications. Future work will focus on the optimization of the design and pulsation parameters with the highlight on the development and practical application of the microreactor.
Figure 8c shows that the pressure drop also pulsates with different amplitudes from the base case and the amplitude of pulsating pressure drop decreases with increasing phase difference, although there is no significant effect on timeaverage pressure drop. This phenomenon can be explained by the pumping power requirement. The total pumping power (PTot) is the sum of pumping power required for air (PA) and gaseous fuel (PF): PTot = PF + PA
(32)
The pumping power is given as Ppump =
Δp . a ·V ηpump
(33)
Since the average pressure drop and average velocity are the same, the average total pumping power required is also the same for all the cases. When the velocity of both air and fuel are in phase, the pressure drop pulsates with high amplitude as pumping power gets added in same magnitude for air and gaseous fuel. The amplitude of pressure drop decreases as the phase difference increases, as the pumping power required for pumping air at any instance of time is either higher or lesser than the gaseous fuel and thus the net amplitude of pressure drop decreases. Similarly the pressure drop is almost constant for a phase difference of π, because at any point of time, if the pumping power required for gaseous fuel is high, for air, it is lesser by the same magnitude, and vice versa. It was also found that conversion rate increases with increase in phase difference between air and fuel and reaches a maximum of 6% at phase differences of 3π/4 and π, and the percentage of pressure drop increases as the phase difference increases. However, there is no effect on outlet temperature, indicating no heat release due to a higher conversion rate, which means that the percentage increase is only due to cumulative error of numerical solution and no actual benefit is gained. 3.4. Effect of Different Forms of Pulsation. Figure 9 shows the inlet velocity profile of air and fuel, the outlet temperature, pressure drop and conversion rate between square and sine waveforms for air inflow pulsations, keeping fuel inflow pulsations to be of sine waveform in both cases. For both cases, the frequency (1 kHz), peak amplitude (0.5 m/s), and phase difference (φ = 0) of different inflow pulsations are maintained same for comparison purposes. For numeric purpose the smooth square waveform was generated by expanding the sine function using the Fourier series up to 1000 odd integer harmonics. As in the case of sine waveforms for both inflow pulsations, there is a gradual increase or decrease in velocity, which also results in gradual increase or decrease in the temperature, conversion rate, and pressure drop. For the case where fuel inflow pulsates with a sine waveform and air inflow pulsates with a square waveform, the temperature, pressure drop, and conversion rate has sudden increase or decrease at every half period and this effect is due to sudden transition in square waveform from high to low velocity or vice versa at every half period of time.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: (514) 398 3788. E-mail addresses: ap.sasmito@gmail. com,
[email protected]. Notes
The authors declare no competing financial interest.
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4. CONCLUDING REMARKS A numerical study was performed to investigate the effect of inflow pulsation parameters, i.e., frequency, amplitude, phase difference, and different pulsation waveforms on the heat and 18709
NOMENCLATURE Ar = pre-exponential factor a = cross-sectional area, m2 Bi = bulk/solid species, mol b′i = stoichiometric coefficient for bulk reactant bi″ = stoichiometric coefficient for bulk product Cp = specific heat, J kg−1 K−1 Cmol = molar concentration, mol m−3 Di = diffusivity of species i, m s−2 Er = activation energy for the reaction, J kg−1 mol−1 Gi = gas species, mol g′i = stoichiometric coefficient for gas reactant g″i = stoichiometric coefficient forgas product ke = effective thermal conductivity, W m−1 K−1 kf,r = reaction rate constant using the Arrhenius expression dx.doi.org/10.1021/ie500797f | Ind. Eng. Chem. Res. 2014, 53, 18699−18710
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M = mean molecular mass ṁ dep = net rate of mass deposition, kg p = pressure, Pa P = pumping power, W Q = volume flow rate, m3 s−1 R = universal gas constant, K kg−1 mol−1 K−1 Ri = reaction rate of species i, kg m−3 Si = surface-adsorbed/site species, mol s′i = stoichiometric coefficient for gas reactant s″i = stoichiometric coefficient for gas product Stemp = heat release/absorption due to reactions, W m−3 T = temperature, K u = velocity, m s−1 V = bulk velocity, m s−1 x = mole fraction Greek Symbols
βr = temperature exponent ρ = density, kg m−3 μ = dynamic viscosity, Pa s−1 ℜ = rate of reaction r ωi = mass fraction of species i η = conversion efficiency ηpump = pump efficiency Subscripts and Superscripts
A = air b = bulk dep = deposition e = effective F = fuel g = gas i = species i r = wall surface reaction s = solid/site temp = temperature tot = total
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