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Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics
Accepted Manuscript Research Paper Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics Sourav Mitra, Mahbubul Muttakin, Kyaw Thu, Bidyut Baran Saha PII: DOI: Reference:
S1359-4311(17)36924-7 https://doi.org/10.1016/j.applthermaleng.2018.01.015 ATE 11669
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
30 October 2017 26 December 2017 4 January 2018
Please cite this article as: S. Mitra, M. Muttakin, K. Thu, B. Baran Saha, Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.01.015
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Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics Sourav Mitra1,2, Mahbubul Muttakin1,4, Kyaw Thu1,4 and Bidyut Baran Saha1,3* 1
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 2
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India
3
Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 4
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga-shi, Fukuoka 816-8580, Japan *
Corresponding author: Tel.: +81-92-802-6722
E-mail: [email protected]
Abstract Adsorption heat exchanger comprises of the adsorbent granules/particles packed in between heat exchanging surfaces. The refrigerant vapor flow as well as heat transfer occurs through the adsorbent column. A 2-dimensional transient CFD study is employed to simulate the adsorption dynamics of ethanol vapor on loosely packed activated carbon. The adsorbent chosen for this study is activated carbon and the refrigerant is ethanol. In this paper, the efficacy of the refrigerant vapor transport through the porous adsorbent bed is studied in terms of flow resistance and thermal diffusion along with the mass diffusion through adsorbent particles. Three heat exchanging domains with same area but different aspect ratios (fin height to fin pitch ratio) along with two particle sizes are evaluated. The dynamic uptake predicted by this CFD study shows strong dependency on flow resistance of porous media for smaller particle size whereas a weak dependency on thermal and intra-particle mass diffusion is observed for larger particles. Furthermore, a comparison on the adsorption dynamics predicted by the present CFD study and
the lumped kinetics model is carried out to determine the validity of the lumped model with respect to the adsorber geometry and particle size.
Keywords: activated carbon; adsorption chiller; CFD; ethanol; heat exchanger
Nomenclature A
pre-exponential factor (s-1)
Cp
specific heat capacity at constant pressure (kJ kg-1 K-1)
dp
particle diameter (m)
Ds
pre-exponential diffusion constant (m2 s-1)
E
characteristic energy for D-A equation (kJ kg-1)
Ea
activation energy (kJ kg-1)
hads
heat of adsorption (kJ kg-1)
hfg
latent heat of evaporation (kJ kg-1)
keff
effective thermal conductivity of adsorbent bed (W m-1 K-1)
n
heterogeneity parameter (-)
p
pressure (kPa)
R
specific gas constant (kJ kg-1 K-1)
t
time (s)
T
temperature (ºC)
u
velocity of vapor in x-direction (m s-1)
v
velocity of vapor in y-direction (m s-1)
X
domain height (m)
Y
domain width (m)
x
coordinate along width of domain (m)
y
coordinate along height of domain (m)
x
grid size along x-direction
y
grid size along x-direction
Greek symbols ε
adsorber bed porosity (-)
λ
permeability of porous adsorbent bed (m2)
μ
viscosity of ethanol vapor (Pa s)
ρ
density (kg m-3)
τ
diffusion time constant (s)
uptake (kg kg-1)
volume averaged uptake (kg kg-1)
*
equilibrium uptake (kg kg-1) normalized uptake (-)
Subscripts I
initiation of adsorption process
II
completion of adsorption process
ads
adsorption
bed cond
adsorber bed condensation
evap
evaporation
max
maximum
min
minimum
v
ethanol vapor
1. Introduction Thermally driven adsorption (AD) chillers have gained significant popularity as a viable alternative to conventional vapor compression chillers. AD chillers are suitable when low grade thermal energy in form of waste heat or solar energy is available; thus, suitable for carbonneutral technology. Additional benefits include zero ozone depletion (ODP) and global warming potential (GWP) as natural refrigerants like water [1], ethanol [2], methanol [3], CO2 [4], ammonia [5] are used; easy maintenance due to absence of moving parts. Despite having these advantages, the bulky structure, low throughput and performance and high cost of manufacturing limits their application [6]. Concerted multi-dimensional research efforts are being carried out to overcome the drawbacks of adsorption chillers. These investigations may be classified as: (i) development of novel adsorbents with high uptake [7–12]; (ii) synthesis of composite adsorbents
to enhance uptake [13–16] and thermal conductivity [17–21] ; (iii) study and optimization of adsorption heat exchanger [22–27]; (iv) adsorption system cycle time manipulation [28–32] along with heat and mass recovery [33–35] to improve efficiency. The present work focusses on investigation of coupled heat and mass transport within an adsorber heat exchanger; hence, a brief review of prior art in this field of adsorption science is presented in the following paragraphs. Two important aspects affect the refrigerant mass transfer in an adsorber heat exchanger: (i) on a macro scale, the inter-particle resistance by the porous adsorbent bed (also known as flow resistance); (ii) on a micro-scale it is the intra-particle mass diffusion resistance. Macro-scale flow resistance arises due to tortuous void space within the packed adsorbent bed through which refrigerant vapor flows [36]; whereas the intra-particle mass diffusion resistance is due to the vapor diffusion through the inherent pores of the adsorbent particle [37]. Thus, combination of these two resistances acting at two different length scales govern the overall uptake of an adsorber heat exchanger. The vapor flow resistance is accounted in the form of permeability and inertial flow resistance of porous media [36]. Several models to estimate intra-particle mass diffusion can be found in literature like linear driving force (LDF) [1], the Fick’s diffusion model [38] and the more recent Langmuir analogy model [39,40]. Practical adsorption chillers employ heat exchangers with extended surfaces to enhance the thermal transport process, with adsorbent particles either loosely packed or coated to these extended surfaces. Several simulation and experimental studies in past have focused on the heat and mass transfer aspect of these heat exchangers. Guilleminot et al. [41] presented a nonisothermal adsorption model for predicting dynamic uptake characteristics. However, isobaric conditions were assumed for this modelling study. Later it was shown that coupled heat and mass transfer model is essential for accurate prediction of adsorption phenomenon in a practical chiller [42,43]. Glaznev and Aristov [22] experimentally studied the effect of cycle boundary conditions on the water adsorption dynamics on loosely packed monolayer of Fuji RD silica gel particles which was followed by experimental study with multi-layers silica gel [44]. A combined experimental and numerical study by Aristov [45] evaluates the effect of water adsorption isotherm shape on dynamic uptake of multi-layered silica gel system. Santamaria et al. [46] experimentally studied water adsorption in AQSOA Z02 zeolite packed in a miniaturized heat exchanger module wherein they found that for grain size 0.15–0.35 mm the throughput is
governed by thermal diffusion and insensitive to grain size. Optimization of fin pitch for silica gel/water chiller was investigated numerically by Rezk and Al-Dadah [23]. Chakraborty et al. [24] simulated the effect of silica gel grain size and number of layers where the thermal and mass diffusion was taken into account. Similar studies were conducted by Mitra et al. [47] for cylindrical shaped silica gel particles. These numerical studies [23,24,47] neglected inter-particle flow resistance and considered only the intra-particle mass diffusion through adsorbent particles in their calculations. Scaling and numerical investigation of water vapor adsorption onto columnar silica gel domain was carried out by Mitra et al. [25]. They derived mathematical expressions for: i) time scale of thermal diffusion in adsorption process; ii) critical length scale of the adsorber domain from inter-particle flow resistance perspective. Niazmand et al. [48–50] carried out several rigorous numerical studies to investigate the effect of fin height, fin pitch and particle size of silica gel/water adsorption pair taking into account flow resistance through adsorber bed as well as mass diffusion within an adsorbent grain. Recently, Jribi et al. [51] numerically investigated the ethanol adsorption onto activated carbon using non-isobaric and non-isothermal conditions to correct the LDF kinetics model. This study was followed by an experimental and numerical study on ethanol adsorption onto finned tube activated carbon heat exchanger assembly [52]. However, these studies do not discuss the effect of important aspects like particle size or heat exchanger geometry on adsorption dynamics. It is evident from the above that majority of the numerical studies for coupled heat and mass transfer studies have been performed for silica gel/water pair and very few work discuss about the activated carbon/ethanol pair. The present work compares the effect of heat exchanger geometry and particle size on the dynamic adsorption characteristics of Maxsorb III/ethanol pair. A 2-dimensional CFD study is carried out for this purpose with the chosen domains representing actual finned heat exchanger configurations. The simulation is carried out for three domains with similar area but different aspect ratios in order to analyze the effect of heat exchanger geometry on flow resistance and thermal diffusion within the adsorbing column. Further, two particle sizes of Maxsorb III are chosen which affects both the macroscopic flow resistance through the porous bed and intra-particle mass diffusion resistance. This study also compares the dynamic uptake as obtained from the 2-dimensional CFD study with 1-dimensional lumped model wherein the domain is assumed to be isothermal and isobaric. This comparison allows for critical
investigation on the efficacy of lumped model for simulating the performance of practical adsorption chillers.
2. Model description This section will describe the physical description of the domain studied, the operating conditions chosen for this study and various assumptions involved in formulating the CFD model.
2.1 Domain description Typically, adsorption heat exchangers are tube-finned assembly with adsorbent packed in between the heat exchanging surfaces. Fig. 1 shows one such assembly wherein the activated carbon (adsorbent) is packed between two consecutive fins and tube surface at the bottom. Heat transfer fluid flows through the tube and ethanol vapor (refrigerant) enters from the top of this assembly. An actual adsorber heat exchanger will contain many such assemblies; however, for the simulation study only one-unit cell can be considered with appropriate boundary conditions (Fig. 1) to reduce the computational time. Thus, the computational domain is a 2-dimensional column with fin height representing the domain height whereas half of fin pitch depicts the width of the domain. Three different domain sizes with the same area are considered; they are: (a) X = 1 mm, Y = 9 mm (Domain I); (b) X = 1.5 mm, Y = 6 mm (Domain II); (c) X = 2 mm, Y = 4.5 mm (Domain III). Domain I has the maximum heat transfer area whereas domain III provides the least resistance to vapor flow. For evaluating the effect of adsorbent grain size, Maxsorb III powder with particle diameters of 30 µm and 70 µm are selected. The thermo-physical properties of the adsorbent (Maxsorb III) used in this study are presented in table 1.
2.2 Operating conditions To initiate the simulation, suitable numerical values for the initial and boundary conditions need to be applied. At the same time the domain must experience appropriate operating conditions to mimic the dynamics of a practical adsorption chiller. In practice an adsorption chiller operates with temperature swing; hence, the adsorption/desorption processes are governed by the imposed temperature jump. Fig. 2 illustrates the adsorption cycle on pressure-uptake chart wherein the heat source temperature Thot is 70°C and heat sink temperature Tcold is 30°C.
The evaporator pressure
p evap
is chosen as 3.2 kPa; which approximately corresponds to
saturation temperature of 10°C. The condenser pressure is given by the saturation pressure corresponding to Tcold and numerically pcond = 10.6 kPa. It must be noted that the present paper only simulates the adsorption process (I–II). Hence, the imposed temperature jump for simulating the adsorption process should not be equal to Thot Tcold ; rather the correct value is given by Tads,i Tcold (Fig. 2). As shown in the figure, a practical adsorption chiller goes through the precooling process prior to the adsorption process. During precooling phase the adsorber temperature reduces to Tads ,i from Thot and simultaneously the adsorber pressure drops from pcond to pevap . Subsequently, ethanol vapor enters the domain at pevap during adsorption process. Therefore,
for the present study, the adsorber domain is initially maintained at temperature, Tads ,i (= 46.5°C) and pressure, pevap (= 3.2 kPa). The initial uptake can therefore be evaluated as I * pevap ,Ta,i ; where * represents the adsorption isotherm for Maxsorb III/ethanol pair. Adsorption process is initiated by the sudden cooling of the isothermal walls (fin and tube) from Ta ,i to Tcold , and the final equilibrium uptake is given by II * pevap ,Tcold . It is apparent that the maximum net uptake
max II I
for the chosen operating conditions is fixed. However, the main goal of this study
is to illustrate the strong dependency of the cooling capacity on dynamic loading of vapor resulted from the adsorber geometry and particle size. It is further noted that the equilibrium uptake is invariant due to the fixed temperature and pressures as well as the adsorbent pair.
2.3 Assumptions Several assumptions are made in the present CFD model in order to simplify the computation process. These are listed as follows: (i)
The heat transfer walls (fin and tube) are assumed to be isothermal. Thus, only the adsorbent domain is simulated in this study and any temperature variation along the fin and tube walls are neglected.
(ii)
Darcy- Forchheimer model for flow through porous media is adopted and the adsorber bed is assumed to be isotropic.
(iii) Thermal equilibrium model for the porous media is adopted i.e. refrigerant (ethanol) vapor and adsorbent (Maxsorb III) are assumed to be at the same temperature. (iv) The adsorbed phase is assumed to behave like liquid and hence, occupies negligible volume. Furthermore, the specific heat capacity of adsorbed phase is assumed to be same as that of liquid phase. (v)
For the operating conditions encountered in this study, the compressibility factor for ethanol is found to be 0.99. Hence, it is prudent to impose ideal gas assumption for vapor phase.
(vi) The thermo-physical properties like bed porosity , thermal conductivity keff
and
viscosity of ethanol vapor are assumed to remain constant throughout the adsorption process. (vii) The variation of heat of adsorption hads with the ethanol uptake is neglected and an average value reported by Uddin et al. [7] is used in this study.
2.4 Mathematical equations The principal mathematical equations consist of mass, momentum and energy conservation equations. To simulate the adsorption process, these conservation equations are modified by adding suitable source terms.
a) Mass balance (continuity) equation
( v ) ( v u ) ( v v) bed 0 t x y t
(1)
where, u and v are the superficial velocity of ethanol vapor along x and y direction. The term
bed
is the mass sink term for vapor phase due to adsorption process. bed represents the t
packing density of Maxsorb III. The rate of uptake represents the adsorption kinetics t due to the diffusion of ethanol vapor through the Maxsorb III micro-pores. There are several models available in literature to describe this phenomenon, amongst which the linear driving force (LDF) model [1] is employed in the present work due to its computational simplicity.
More rigorous adsorption kinetics models [38–40] are computationally intensive and hence, not implemented in the present CFD model. The mathematical form of the LDF equation is:
( ) t
(2)
where the equilibrium uptake * is determined by the Dubinin-Astakhov (D-A) adsorption isotherm equation: RT p max exp ln sat E p
n
(3)
The time constant in Eq. (2) also known as diffusion time constant governs the rate of adsorption. This time constant provides an estimate of intra-particle mass transfer resistance and is dependent on the particle size d p , diffusion constant of ethanol vapor through the adsorbent Ds and the instantaneous temperature T :
d p2 E 60 Ds exp a RT
(4)
It is expected that as the adsorbent particle size increases the vapor penetration length scale increases thereby leading to larger diffusion time constant. This is also evident from Eq. (4). On the contrary, any increase in diffusivity of vapor will reduce and hence accelerate the adsorption process.
b) Momentum balance equation x momentum:
1 ( v u ) u ( v u ) v ( v u ) p 2u 2u 1 2 2 2 2 u v u u t x y x x y 2
(5)
y momentum: 1 ( v v ) u ( v v ) v ( v v) p 2v 2v 1 2 2 2 2 v v v v t x y y x y 2
(6)
The viscous flow resistance due to porous media is the reciprocal of effective permeability
of the adsorbent bed which is determined from Ergun equation [36]:
3d p2 150(1 ) 2
(7)
The inertial flow resistance is given by:
3.5(1 ) d p 3
(8)
The above equations provide a relationship between adsorbent particle size d p and interparticle flow resistance. Smaller particle size reduces the permeability of the bed and hence increases the flow resistance through the voids which should eventually manifest as larger pressure drop within the domain. Additionally, decrease in particle size increases the inertial flow resistance . Thus, any reduction in particle size should adversely affect the overall flow resistance and increase the pressure drop within the bed. The pressure p and density of refrigerant vapor v are related by the ideal gas equation:
p v RT
(9)
c) Energy balance equation
(vC p ,v bed C p ,bed )
T T T v C p ,v u v keff t y x
2T 2T 2 2 y x
hads bed t
(10)
The first term on the LHS denotes the unsteady term due to thermal mass whereas the second term represents energy transfer due to convection. The first term on RHS is the thermal diffusion term wherein the effective bed thermal conductivity is evaluated as volume average of thermal conductivities of ethanol vapor and Maxsorb III. The last term on RHS is the heat source term which accounts for the energy released during adsorption process (heat of adsorption).
3. Solution procedure 3.1 Numerical implementation The CFD study is carried out using ANSYS® Fluent (version 14.0), employing user defined functions (UDF) for appropriate source terms in continuity and energy equations. Time and grid independency studies were carried out and constant time step of 10 -3 s was found to be suitable
whereas a square grid x y of 0.05 mm side is used for each domain. The SIMPLE algorithm [53] is employed to solve the continuity and momentum equations. The saturation pressure for the ethanol is predicted using Antoinne equation: log10 ps A
B T C
(11)
The numerical values of Antoinne parameters A, B and C for ethanol are 5.2468, 1598.673 and 46.424 respectively. Table 1 lists all the important parameters of the Maxsorb III/ethanol adsorption pair.
3.2 Validation of the model The numerical model is validated with experimental data reported by Jribi et al. [52] for the dynamic ethanol uptake onto Maxsorb III packed tube-fin assembly. The mean particle size is 70 µm and the heat exchanger assembly has a fin pitch of 3.7 mm with fin height (adsorbent thickness) of 10 mm. Adsorption occurs at 20°C while desorption temperature is 80°C with evaporator pressure of 3.85 kPa and condenser pressure at 10.35 kPa. Computational domain and boundary conditions chosen for this study are as described in their work. Fig. 3 depicts the comparison of experimental and simulated temperature plot at the mid-point of heat exchanging domain during the adsorption process. A close agreement between the two curves validates the model.
4. Results and discussion 4.1 Effect of domain size The pressure, temperature and uptake contours for various domains at t =10 s are shown in Fig. 4 a), b) and c) respectively for fixed particle size of 30 µm. It is evident from Fig. 4 a) and b) that the slender domain i.e. domain I has the adverse pressure gradient developed within it whereas the domain III, which has the widest vapor entry region, exhibits minimum pressure drop. Conversely, domain I owing to its highest heat transfer surface X Y , has uniform temperature contours when compared to domain III. From Fig. 4 c) it is evident that domain I exhibits the minimum uptake near the bottom part while domain III has lowest uptake near the central part. These low uptake regions can be attributed to the presence of low pressure region near the bottom of domain I (Fig. 4 a)) whereas for domain III it is the high temperature region
away from the cold wall (Fig. 4 b)). This illustrates the counteracting effect of temperature and pressure contours on the spatial adsorption uptake based on the domain aspect ratio. To investigate the net effect of domain aspect ratio on the dynamic adsorption characteristics, the volumetric average uptake is evaluated at each time step. The volumetric uptake for each domain is calculated as:
xy i i
(12)
XY
Fig. 5 shows the temporal variation of normalized uptake for each domain with particle size of 30 µm. It is apparent from the figures that domain III with widest vapor entry region exhibits the best performance, whereas the domain I with tallest fin height shows the poorest results. Fig. 6 a) and b) show the pressure drop and average domain temperature plots respectively. It is evident that domain I has significantly higher pressure drop amongst all the studied configurations; concomitantly it also shows the fastest cooling rate. Thus, it is obvious that the flow resistance by the porous bed plays a more significant role in defining the adsorption dynamics than the cooling rate. In fact a theoretical study [25] of flow through columnar adsorber domain revealed that the limiting aspect ratio for an adsorber domain is given by the following relationship: 0.5
Y pevap evap hads X keff Tads ,i Tcold
(13)
If the domain has a higher aspect ratio, the uptake is limited due to pressure drop experienced by the bed during adsorption process. For the present operating conditions and particle size of 30 µm, this critical limit for aspect ratio is found to be 4. This further explains the observed deterioration for domain I when compared to domain III which agrees well with the above relation.
4.2 Effect of particle size To evaluate the relative importance of the intra-particle mass transfer resistance with respect to the flow resistance, CFD studies were performed for larger particle size i.e. 70 µm and the results were compared to 30 µm studies. The increase in particle size has two contradicting effects:
(i)
Decrease in the flow resistance as bigger particles result in the increased permeability of the porous bed (Eq. (7)). This should result in the enhancement of adsorption phenomenon;
(ii)
Increased mass diffusion time constant (Eq. (4)) or in other words slower adsorption kinetics due to large mass transfer length scale d p .
Fig. 7 a) and b) compare the pressure drop and the temperature profiles for the three domains with different particle sizes. As mentioned above, the gradient of the pressure drop for 70 µm particle size domains are insignificant when compared to 30 µm. On the other hand the cooling curves are significantly steeper for 70 µm particle size which may be attributed to lower heat of
adsorption released due to slower mass diffusion . The adsorption uptake curves (Fig. 8) t illustrate that for 70 µm particle size there is insignificant effect of domain aspect ratio on the adsorption dynamics, signifying that the system is mass diffusion limited rather than by flow resistance of the bed. It is also interesting to note the correlation between domain cooling curves and adsorption dynamics for 70 µm particle size. Domain I with fastest cooling curve shows fastest adsorption dynamics whereas domain III with slowest cooling curve is the slowest. This observation is in contrast to 30 µm particle size, wherein domain I exhibits the slowest and domain III the fastest adsorption dynamics. Thus, it can be concluded that for smaller particle size, the adsorption dynamics is limited predominantly by flow resistance whereas for larger particles it is the combination of thermal diffusion through the bed and intra-particle mass diffusion which governs the adsorption dynamics. Fig. 8 also depicts that the adsorption dynamics for 30 µm particle is generally faster than 70 µm owing to faster kinetics except for domain I. Revisiting the equation for critical aspect ratio (Eq. (13)) for 70 µm particle size yields a numerical value of 9 and hence, the inequality equation is satisfied by all the domains considered in this study. On the contrary, for 30 µm particle size domain I does not satisfy the inequality condition and shows the anomalous behavior. This further emphasizes on the adverse effect of pressure drop on adsorption dynamics. Thus, during the design of adsorption heat exchanger, one may use inequality Eq. (13) as a guiding principle to optimize the fin height to its pitch ratio.
4.3 Specific cooling capacity The main objective to study the adsorber domain is to predict the cooling capacity based on the adsorption dynamics. Theoretical specific cooling capacity (SCC) for each domain can be estimated by the following mathematical relationship: SCC
0.8 II I h fg t0.8
(14)
Here, II I represents the maximum uptake by the domain. Any adsorption system will take infinitely long time to achieve the saturation uptake of II ; hence, practical adsorption chillers operate with a finite cycle time. In this paper, 80% of maximum uptake is adopted to determine the adsorption cycle time t0.8 as in done in many previous studies . Table 2 shows the SCC for the selected domains and the particle size considered in this study. The CFD study shows that for the present operating conditions and heat exchanger geometry, the SCC ranges between 424 and 710 W/kg. It can be observed that the maximum cooling capacity with 30 μm particle size can be obtained using domain III whereas domain I is best suited for 70 μm particles. For smaller particle size, uptake is limited by flow resistance hence, a domain with smaller height is preferable; whereas adsorber with larger particle size is limited by thermal transport thereby requiring a domain with larger heat transfer surface. Therefore, it can be concluded that the optimum heat exchanger geometry is dependent on the particle size chosen. Further, it must be noted that the trend for cooling capacity closely imitates the adsorption dynamics seen in Fig. 8.
4.4 Comparison with lumped model Even though a 2-dimensional rigorous CFD model is essential to predict the adsorption dynamics of a practical chiller, the intensive computational requirement limits its utilization. Majority of the studies still use the lumped model to predict adsorption dynamics where the spatial variation of pressure and temperature are neglected for computational simplification. In other words, the heat exchanging domain is assumed to be near isobaric and isothermal. In this scenario, one can predict the temporal variation of uptake by merely integrating the LDF equation (Eq.(2)) which yields an exponential function:
1 e
t
(15)
Where the normalized uptake is represented as:
I II I
(16)
Similarly, the normalized average uptake
for each domain may be defined as:
I II I
(17)
Here, represents the spatial averaged uptake for each domain. Fig. 9 compares the normalized uptake predicted by the lumped LDF model calculated from Eq. (15) with average normalized uptake obtained from the CFD simulation results for each domain and particle size. The non-dimensional time
t is chosen for this comparison. The figure shows that
lumped LDF model over predicts the adsorption uptake for all configurations. This model incurs significant error for smaller particle size attributed to the large pressure drop that occurs in such situation and therefore the isobaric assumption is not valid. This deviation reduces as the particle size increases. Nevertheless, the marginal error for larger particle size occurs due to the nonisothermal nature of the domain. It can also be observed that the lumped model is more accurate in predicting the adsorption dynamics for smaller aspect ratio (wider domain). Thus, it can be concluded that the lumped LDF model may be used with reasonable accuracy for adsorption chillers with large adsorbent particle size and small aspect ratio.
5. Conclusion This paper investigates the presence of optimum heat exchanger geometry with respect to the adsorbent particle size elucidating the bottlenecks due to intra-particle mass diffusion, interparticle flow resistance and thermal transport. An adsorption system using ethanol and activated carbon (Maxsorb-III) is selected for this purpose. CFD study of a 2-dimensional configuration is employed to investigate the spatial variation of thermodynamic parameters within the domain. Three domains with the same area but different aspect ratios (2.25, 4 and 9) are considered along with two particle sizes (30 and 70 µm). The study indicates that based on the particle size and aspect ratio, certain domains are limited by vapor transport while others are limited by thermal and intra-particle mass diffusion. Further, it is shown that the use of smaller particle size does not
always lead to enhanced adsorption dynamics as the ratio of fin height to its pitch (aspect ratio) also plays an important role. The domain aspect ratio should remain lower than a critical value for maximizing the adsorption dynamics. Specific cooling capacity (SCC) derived from simulation results indicate the existence of optimum heat exchanging geometry for a particular particle size. Taller domain is preferable for larger particle size whereas wider domain is suitable for smaller particle size. The SCC calculated for the present study ranges between 424 to 710 W/kg of Maxsorb III. A comparison of CFD results with the lumped (isothermal and isobaric) model reveals significant deviation between the two. This deviation is minimum when the adsorbent particle size is large and a wide domain (small fin height to fin pitch ratio) is chosen for the adsorption process.
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Pressure inlet
Domain boundary
Vapour inlet
Fins
Symmetry Adsorbent bed
Y
Isothermal y walls
Tube surface
X
x Adsorber heat exchanging unit
Domain boundary conditions
Fig. 1: Adsorber domain boundary conditions
Uptake (kg kg-1 )
1.4
1.2
30°C 46.5°C
1.0
II
70°C
III
max
0.8 Tcold 0.6 0.4
I
IV Thot
Tads,i
0.2 pevap
pcond
0.0 1
2
3
4
5 6 7 Pressure (kPa)
8
9
Fig. 2: Operating and initial conditions on adsorption pressure-uptake plot
10
11
40 Simulation result
38
Temperature (ºC)
Experimental data 36 34 32 30 28 26 0
50
100
150 Time (s)
200
250
300
Fig. 3: Comparison of simulated temperature curve with experimental data [52] for ethanol adsorption onto activated carbon packed tube-fin assembly
a)
Domain I Pressure (kPa)
Domain II
Domain III
b)
Domain I Temperature ( C)
Domain II
Domain III
c)
Domain I Uptake (kg kg-1)
Domain II
Domain III
Fig. 4: a) Pressure b) temperature c) uptake contour plots at t = 10 s and dp = 30 µm
Fig. 5: Adsorption dynamics for various domains and dp = 30 µm
a)
b)
Fig. 6: Temporal plots of a) Pressure drop b) average domain temperature for dp = 30 µm
a)
b)
Fig. 7: Temporal plots comparing the a) pressure drop b) average domain temperature for 30 µm and 70 µm particle sizes
Fig. 8: Dynamics adsorption characteristics for various domains and particle size
Fig. 9: Comparison of normalized uptake obtained from lumped LDF model and as obtained from the present CFD study for various domains and particle sizes
Table 1: Numerical value of parameters used in this study Parameter
Value
Total surface area
3045 m2 g-1
Micro-pore volume
1.7 cm3 g-1
Average pore width
1.12 nm
Characteristic energy for D-A equation E
139.5 kJ kg-1 [54]
Maximum uptake max
1.2 kg kg-1
Heterogeneity parameter n
1.8
Activation energy Ea
225 kJ kg-1 [54]
Pre-exponential diffusion constant Ds
1.972×10-11 m2s-1
Specific heat capacity C p ,bed
0.82 kJ kg-1 K-1
Thermal conductivity keff
0.066 W m-1 K-1 [20]
Bed porosity
0.38
Packing density bed
290 kg m-3
Heat of adsorption hads
1002 kJ kg-1 [7]
Table 2: Specific cooling capacity for all the domains and particle sizes Specific Cooling Capacity (W/kg) Particle size (µm)
Domain I
Domain II
Domain III
30
424
682
710
70
517
493
445
Highlights
A 2-D transient study on adsorption dynamics of ethanol onto Maxsorb III is conducted.
Mass transfer limits adsorption dynamics in high aspect ratio heat exchanger geometry.
Heat transfer limits adsorption dynamics for small aspect ratio heat exchangers.
Higher aspect ratio is preferable for larger adsorbent particle size.
Lumped LDF model leads to erroneous results for smaller particles and high aspect ratio geometry.
S1359-4311(17)36924-7 https://doi.org/10.1016/j.applthermaleng.2018.01.015 ATE 11669
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
30 October 2017 26 December 2017 4 January 2018
Please cite this article as: S. Mitra, M. Muttakin, K. Thu, B. Baran Saha, Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.01.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study on the influence of adsorbent particle size and heat exchanger aspect ratio on dynamic adsorption characteristics Sourav Mitra1,2, Mahbubul Muttakin1,4, Kyaw Thu1,4 and Bidyut Baran Saha1,3* 1
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 2
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur 721302, India
3
Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan 4
Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga-shi, Fukuoka 816-8580, Japan *
Corresponding author: Tel.: +81-92-802-6722
E-mail: [email protected]
Abstract Adsorption heat exchanger comprises of the adsorbent granules/particles packed in between heat exchanging surfaces. The refrigerant vapor flow as well as heat transfer occurs through the adsorbent column. A 2-dimensional transient CFD study is employed to simulate the adsorption dynamics of ethanol vapor on loosely packed activated carbon. The adsorbent chosen for this study is activated carbon and the refrigerant is ethanol. In this paper, the efficacy of the refrigerant vapor transport through the porous adsorbent bed is studied in terms of flow resistance and thermal diffusion along with the mass diffusion through adsorbent particles. Three heat exchanging domains with same area but different aspect ratios (fin height to fin pitch ratio) along with two particle sizes are evaluated. The dynamic uptake predicted by this CFD study shows strong dependency on flow resistance of porous media for smaller particle size whereas a weak dependency on thermal and intra-particle mass diffusion is observed for larger particles. Furthermore, a comparison on the adsorption dynamics predicted by the present CFD study and
the lumped kinetics model is carried out to determine the validity of the lumped model with respect to the adsorber geometry and particle size.
Keywords: activated carbon; adsorption chiller; CFD; ethanol; heat exchanger
Nomenclature A
pre-exponential factor (s-1)
Cp
specific heat capacity at constant pressure (kJ kg-1 K-1)
dp
particle diameter (m)
Ds
pre-exponential diffusion constant (m2 s-1)
E
characteristic energy for D-A equation (kJ kg-1)
Ea
activation energy (kJ kg-1)
hads
heat of adsorption (kJ kg-1)
hfg
latent heat of evaporation (kJ kg-1)
keff
effective thermal conductivity of adsorbent bed (W m-1 K-1)
n
heterogeneity parameter (-)
p
pressure (kPa)
R
specific gas constant (kJ kg-1 K-1)
t
time (s)
T
temperature (ºC)
u
velocity of vapor in x-direction (m s-1)
v
velocity of vapor in y-direction (m s-1)
X
domain height (m)
Y
domain width (m)
x
coordinate along width of domain (m)
y
coordinate along height of domain (m)
x
grid size along x-direction
y
grid size along x-direction
Greek symbols ε
adsorber bed porosity (-)
λ
permeability of porous adsorbent bed (m2)
μ
viscosity of ethanol vapor (Pa s)
ρ
density (kg m-3)
τ
diffusion time constant (s)
uptake (kg kg-1)
volume averaged uptake (kg kg-1)
*
equilibrium uptake (kg kg-1) normalized uptake (-)
Subscripts I
initiation of adsorption process
II
completion of adsorption process
ads
adsorption
bed cond
adsorber bed condensation
evap
evaporation
max
maximum
min
minimum
v
ethanol vapor
1. Introduction Thermally driven adsorption (AD) chillers have gained significant popularity as a viable alternative to conventional vapor compression chillers. AD chillers are suitable when low grade thermal energy in form of waste heat or solar energy is available; thus, suitable for carbonneutral technology. Additional benefits include zero ozone depletion (ODP) and global warming potential (GWP) as natural refrigerants like water [1], ethanol [2], methanol [3], CO2 [4], ammonia [5] are used; easy maintenance due to absence of moving parts. Despite having these advantages, the bulky structure, low throughput and performance and high cost of manufacturing limits their application [6]. Concerted multi-dimensional research efforts are being carried out to overcome the drawbacks of adsorption chillers. These investigations may be classified as: (i) development of novel adsorbents with high uptake [7–12]; (ii) synthesis of composite adsorbents
to enhance uptake [13–16] and thermal conductivity [17–21] ; (iii) study and optimization of adsorption heat exchanger [22–27]; (iv) adsorption system cycle time manipulation [28–32] along with heat and mass recovery [33–35] to improve efficiency. The present work focusses on investigation of coupled heat and mass transport within an adsorber heat exchanger; hence, a brief review of prior art in this field of adsorption science is presented in the following paragraphs. Two important aspects affect the refrigerant mass transfer in an adsorber heat exchanger: (i) on a macro scale, the inter-particle resistance by the porous adsorbent bed (also known as flow resistance); (ii) on a micro-scale it is the intra-particle mass diffusion resistance. Macro-scale flow resistance arises due to tortuous void space within the packed adsorbent bed through which refrigerant vapor flows [36]; whereas the intra-particle mass diffusion resistance is due to the vapor diffusion through the inherent pores of the adsorbent particle [37]. Thus, combination of these two resistances acting at two different length scales govern the overall uptake of an adsorber heat exchanger. The vapor flow resistance is accounted in the form of permeability and inertial flow resistance of porous media [36]. Several models to estimate intra-particle mass diffusion can be found in literature like linear driving force (LDF) [1], the Fick’s diffusion model [38] and the more recent Langmuir analogy model [39,40]. Practical adsorption chillers employ heat exchangers with extended surfaces to enhance the thermal transport process, with adsorbent particles either loosely packed or coated to these extended surfaces. Several simulation and experimental studies in past have focused on the heat and mass transfer aspect of these heat exchangers. Guilleminot et al. [41] presented a nonisothermal adsorption model for predicting dynamic uptake characteristics. However, isobaric conditions were assumed for this modelling study. Later it was shown that coupled heat and mass transfer model is essential for accurate prediction of adsorption phenomenon in a practical chiller [42,43]. Glaznev and Aristov [22] experimentally studied the effect of cycle boundary conditions on the water adsorption dynamics on loosely packed monolayer of Fuji RD silica gel particles which was followed by experimental study with multi-layers silica gel [44]. A combined experimental and numerical study by Aristov [45] evaluates the effect of water adsorption isotherm shape on dynamic uptake of multi-layered silica gel system. Santamaria et al. [46] experimentally studied water adsorption in AQSOA Z02 zeolite packed in a miniaturized heat exchanger module wherein they found that for grain size 0.15–0.35 mm the throughput is
governed by thermal diffusion and insensitive to grain size. Optimization of fin pitch for silica gel/water chiller was investigated numerically by Rezk and Al-Dadah [23]. Chakraborty et al. [24] simulated the effect of silica gel grain size and number of layers where the thermal and mass diffusion was taken into account. Similar studies were conducted by Mitra et al. [47] for cylindrical shaped silica gel particles. These numerical studies [23,24,47] neglected inter-particle flow resistance and considered only the intra-particle mass diffusion through adsorbent particles in their calculations. Scaling and numerical investigation of water vapor adsorption onto columnar silica gel domain was carried out by Mitra et al. [25]. They derived mathematical expressions for: i) time scale of thermal diffusion in adsorption process; ii) critical length scale of the adsorber domain from inter-particle flow resistance perspective. Niazmand et al. [48–50] carried out several rigorous numerical studies to investigate the effect of fin height, fin pitch and particle size of silica gel/water adsorption pair taking into account flow resistance through adsorber bed as well as mass diffusion within an adsorbent grain. Recently, Jribi et al. [51] numerically investigated the ethanol adsorption onto activated carbon using non-isobaric and non-isothermal conditions to correct the LDF kinetics model. This study was followed by an experimental and numerical study on ethanol adsorption onto finned tube activated carbon heat exchanger assembly [52]. However, these studies do not discuss the effect of important aspects like particle size or heat exchanger geometry on adsorption dynamics. It is evident from the above that majority of the numerical studies for coupled heat and mass transfer studies have been performed for silica gel/water pair and very few work discuss about the activated carbon/ethanol pair. The present work compares the effect of heat exchanger geometry and particle size on the dynamic adsorption characteristics of Maxsorb III/ethanol pair. A 2-dimensional CFD study is carried out for this purpose with the chosen domains representing actual finned heat exchanger configurations. The simulation is carried out for three domains with similar area but different aspect ratios in order to analyze the effect of heat exchanger geometry on flow resistance and thermal diffusion within the adsorbing column. Further, two particle sizes of Maxsorb III are chosen which affects both the macroscopic flow resistance through the porous bed and intra-particle mass diffusion resistance. This study also compares the dynamic uptake as obtained from the 2-dimensional CFD study with 1-dimensional lumped model wherein the domain is assumed to be isothermal and isobaric. This comparison allows for critical
investigation on the efficacy of lumped model for simulating the performance of practical adsorption chillers.
2. Model description This section will describe the physical description of the domain studied, the operating conditions chosen for this study and various assumptions involved in formulating the CFD model.
2.1 Domain description Typically, adsorption heat exchangers are tube-finned assembly with adsorbent packed in between the heat exchanging surfaces. Fig. 1 shows one such assembly wherein the activated carbon (adsorbent) is packed between two consecutive fins and tube surface at the bottom. Heat transfer fluid flows through the tube and ethanol vapor (refrigerant) enters from the top of this assembly. An actual adsorber heat exchanger will contain many such assemblies; however, for the simulation study only one-unit cell can be considered with appropriate boundary conditions (Fig. 1) to reduce the computational time. Thus, the computational domain is a 2-dimensional column with fin height representing the domain height whereas half of fin pitch depicts the width of the domain. Three different domain sizes with the same area are considered; they are: (a) X = 1 mm, Y = 9 mm (Domain I); (b) X = 1.5 mm, Y = 6 mm (Domain II); (c) X = 2 mm, Y = 4.5 mm (Domain III). Domain I has the maximum heat transfer area whereas domain III provides the least resistance to vapor flow. For evaluating the effect of adsorbent grain size, Maxsorb III powder with particle diameters of 30 µm and 70 µm are selected. The thermo-physical properties of the adsorbent (Maxsorb III) used in this study are presented in table 1.
2.2 Operating conditions To initiate the simulation, suitable numerical values for the initial and boundary conditions need to be applied. At the same time the domain must experience appropriate operating conditions to mimic the dynamics of a practical adsorption chiller. In practice an adsorption chiller operates with temperature swing; hence, the adsorption/desorption processes are governed by the imposed temperature jump. Fig. 2 illustrates the adsorption cycle on pressure-uptake chart wherein the heat source temperature Thot is 70°C and heat sink temperature Tcold is 30°C.
The evaporator pressure
p evap
is chosen as 3.2 kPa; which approximately corresponds to
saturation temperature of 10°C. The condenser pressure is given by the saturation pressure corresponding to Tcold and numerically pcond = 10.6 kPa. It must be noted that the present paper only simulates the adsorption process (I–II). Hence, the imposed temperature jump for simulating the adsorption process should not be equal to Thot Tcold ; rather the correct value is given by Tads,i Tcold (Fig. 2). As shown in the figure, a practical adsorption chiller goes through the precooling process prior to the adsorption process. During precooling phase the adsorber temperature reduces to Tads ,i from Thot and simultaneously the adsorber pressure drops from pcond to pevap . Subsequently, ethanol vapor enters the domain at pevap during adsorption process. Therefore,
for the present study, the adsorber domain is initially maintained at temperature, Tads ,i (= 46.5°C) and pressure, pevap (= 3.2 kPa). The initial uptake can therefore be evaluated as I * pevap ,Ta,i ; where * represents the adsorption isotherm for Maxsorb III/ethanol pair. Adsorption process is initiated by the sudden cooling of the isothermal walls (fin and tube) from Ta ,i to Tcold , and the final equilibrium uptake is given by II * pevap ,Tcold . It is apparent that the maximum net uptake
max II I
for the chosen operating conditions is fixed. However, the main goal of this study
is to illustrate the strong dependency of the cooling capacity on dynamic loading of vapor resulted from the adsorber geometry and particle size. It is further noted that the equilibrium uptake is invariant due to the fixed temperature and pressures as well as the adsorbent pair.
2.3 Assumptions Several assumptions are made in the present CFD model in order to simplify the computation process. These are listed as follows: (i)
The heat transfer walls (fin and tube) are assumed to be isothermal. Thus, only the adsorbent domain is simulated in this study and any temperature variation along the fin and tube walls are neglected.
(ii)
Darcy- Forchheimer model for flow through porous media is adopted and the adsorber bed is assumed to be isotropic.
(iii) Thermal equilibrium model for the porous media is adopted i.e. refrigerant (ethanol) vapor and adsorbent (Maxsorb III) are assumed to be at the same temperature. (iv) The adsorbed phase is assumed to behave like liquid and hence, occupies negligible volume. Furthermore, the specific heat capacity of adsorbed phase is assumed to be same as that of liquid phase. (v)
For the operating conditions encountered in this study, the compressibility factor for ethanol is found to be 0.99. Hence, it is prudent to impose ideal gas assumption for vapor phase.
(vi) The thermo-physical properties like bed porosity , thermal conductivity keff
and
viscosity of ethanol vapor are assumed to remain constant throughout the adsorption process. (vii) The variation of heat of adsorption hads with the ethanol uptake is neglected and an average value reported by Uddin et al. [7] is used in this study.
2.4 Mathematical equations The principal mathematical equations consist of mass, momentum and energy conservation equations. To simulate the adsorption process, these conservation equations are modified by adding suitable source terms.
a) Mass balance (continuity) equation
( v ) ( v u ) ( v v) bed 0 t x y t
(1)
where, u and v are the superficial velocity of ethanol vapor along x and y direction. The term
bed
is the mass sink term for vapor phase due to adsorption process. bed represents the t
packing density of Maxsorb III. The rate of uptake represents the adsorption kinetics t due to the diffusion of ethanol vapor through the Maxsorb III micro-pores. There are several models available in literature to describe this phenomenon, amongst which the linear driving force (LDF) model [1] is employed in the present work due to its computational simplicity.
More rigorous adsorption kinetics models [38–40] are computationally intensive and hence, not implemented in the present CFD model. The mathematical form of the LDF equation is:
( ) t
(2)
where the equilibrium uptake * is determined by the Dubinin-Astakhov (D-A) adsorption isotherm equation: RT p max exp ln sat E p
n
(3)
The time constant in Eq. (2) also known as diffusion time constant governs the rate of adsorption. This time constant provides an estimate of intra-particle mass transfer resistance and is dependent on the particle size d p , diffusion constant of ethanol vapor through the adsorbent Ds and the instantaneous temperature T :
d p2 E 60 Ds exp a RT
(4)
It is expected that as the adsorbent particle size increases the vapor penetration length scale increases thereby leading to larger diffusion time constant. This is also evident from Eq. (4). On the contrary, any increase in diffusivity of vapor will reduce and hence accelerate the adsorption process.
b) Momentum balance equation x momentum:
1 ( v u ) u ( v u ) v ( v u ) p 2u 2u 1 2 2 2 2 u v u u t x y x x y 2
(5)
y momentum: 1 ( v v ) u ( v v ) v ( v v) p 2v 2v 1 2 2 2 2 v v v v t x y y x y 2
(6)
The viscous flow resistance due to porous media is the reciprocal of effective permeability
of the adsorbent bed which is determined from Ergun equation [36]:
3d p2 150(1 ) 2
(7)
The inertial flow resistance is given by:
3.5(1 ) d p 3
(8)
The above equations provide a relationship between adsorbent particle size d p and interparticle flow resistance. Smaller particle size reduces the permeability of the bed and hence increases the flow resistance through the voids which should eventually manifest as larger pressure drop within the domain. Additionally, decrease in particle size increases the inertial flow resistance . Thus, any reduction in particle size should adversely affect the overall flow resistance and increase the pressure drop within the bed. The pressure p and density of refrigerant vapor v are related by the ideal gas equation:
p v RT
(9)
c) Energy balance equation
(vC p ,v bed C p ,bed )
T T T v C p ,v u v keff t y x
2T 2T 2 2 y x
hads bed t
(10)
The first term on the LHS denotes the unsteady term due to thermal mass whereas the second term represents energy transfer due to convection. The first term on RHS is the thermal diffusion term wherein the effective bed thermal conductivity is evaluated as volume average of thermal conductivities of ethanol vapor and Maxsorb III. The last term on RHS is the heat source term which accounts for the energy released during adsorption process (heat of adsorption).
3. Solution procedure 3.1 Numerical implementation The CFD study is carried out using ANSYS® Fluent (version 14.0), employing user defined functions (UDF) for appropriate source terms in continuity and energy equations. Time and grid independency studies were carried out and constant time step of 10 -3 s was found to be suitable
whereas a square grid x y of 0.05 mm side is used for each domain. The SIMPLE algorithm [53] is employed to solve the continuity and momentum equations. The saturation pressure for the ethanol is predicted using Antoinne equation: log10 ps A
B T C
(11)
The numerical values of Antoinne parameters A, B and C for ethanol are 5.2468, 1598.673 and 46.424 respectively. Table 1 lists all the important parameters of the Maxsorb III/ethanol adsorption pair.
3.2 Validation of the model The numerical model is validated with experimental data reported by Jribi et al. [52] for the dynamic ethanol uptake onto Maxsorb III packed tube-fin assembly. The mean particle size is 70 µm and the heat exchanger assembly has a fin pitch of 3.7 mm with fin height (adsorbent thickness) of 10 mm. Adsorption occurs at 20°C while desorption temperature is 80°C with evaporator pressure of 3.85 kPa and condenser pressure at 10.35 kPa. Computational domain and boundary conditions chosen for this study are as described in their work. Fig. 3 depicts the comparison of experimental and simulated temperature plot at the mid-point of heat exchanging domain during the adsorption process. A close agreement between the two curves validates the model.
4. Results and discussion 4.1 Effect of domain size The pressure, temperature and uptake contours for various domains at t =10 s are shown in Fig. 4 a), b) and c) respectively for fixed particle size of 30 µm. It is evident from Fig. 4 a) and b) that the slender domain i.e. domain I has the adverse pressure gradient developed within it whereas the domain III, which has the widest vapor entry region, exhibits minimum pressure drop. Conversely, domain I owing to its highest heat transfer surface X Y , has uniform temperature contours when compared to domain III. From Fig. 4 c) it is evident that domain I exhibits the minimum uptake near the bottom part while domain III has lowest uptake near the central part. These low uptake regions can be attributed to the presence of low pressure region near the bottom of domain I (Fig. 4 a)) whereas for domain III it is the high temperature region
away from the cold wall (Fig. 4 b)). This illustrates the counteracting effect of temperature and pressure contours on the spatial adsorption uptake based on the domain aspect ratio. To investigate the net effect of domain aspect ratio on the dynamic adsorption characteristics, the volumetric average uptake is evaluated at each time step. The volumetric uptake for each domain is calculated as:
xy i i
(12)
XY
Fig. 5 shows the temporal variation of normalized uptake for each domain with particle size of 30 µm. It is apparent from the figures that domain III with widest vapor entry region exhibits the best performance, whereas the domain I with tallest fin height shows the poorest results. Fig. 6 a) and b) show the pressure drop and average domain temperature plots respectively. It is evident that domain I has significantly higher pressure drop amongst all the studied configurations; concomitantly it also shows the fastest cooling rate. Thus, it is obvious that the flow resistance by the porous bed plays a more significant role in defining the adsorption dynamics than the cooling rate. In fact a theoretical study [25] of flow through columnar adsorber domain revealed that the limiting aspect ratio for an adsorber domain is given by the following relationship: 0.5
Y pevap evap hads X keff Tads ,i Tcold
(13)
If the domain has a higher aspect ratio, the uptake is limited due to pressure drop experienced by the bed during adsorption process. For the present operating conditions and particle size of 30 µm, this critical limit for aspect ratio is found to be 4. This further explains the observed deterioration for domain I when compared to domain III which agrees well with the above relation.
4.2 Effect of particle size To evaluate the relative importance of the intra-particle mass transfer resistance with respect to the flow resistance, CFD studies were performed for larger particle size i.e. 70 µm and the results were compared to 30 µm studies. The increase in particle size has two contradicting effects:
(i)
Decrease in the flow resistance as bigger particles result in the increased permeability of the porous bed (Eq. (7)). This should result in the enhancement of adsorption phenomenon;
(ii)
Increased mass diffusion time constant (Eq. (4)) or in other words slower adsorption kinetics due to large mass transfer length scale d p .
Fig. 7 a) and b) compare the pressure drop and the temperature profiles for the three domains with different particle sizes. As mentioned above, the gradient of the pressure drop for 70 µm particle size domains are insignificant when compared to 30 µm. On the other hand the cooling curves are significantly steeper for 70 µm particle size which may be attributed to lower heat of
adsorption released due to slower mass diffusion . The adsorption uptake curves (Fig. 8) t illustrate that for 70 µm particle size there is insignificant effect of domain aspect ratio on the adsorption dynamics, signifying that the system is mass diffusion limited rather than by flow resistance of the bed. It is also interesting to note the correlation between domain cooling curves and adsorption dynamics for 70 µm particle size. Domain I with fastest cooling curve shows fastest adsorption dynamics whereas domain III with slowest cooling curve is the slowest. This observation is in contrast to 30 µm particle size, wherein domain I exhibits the slowest and domain III the fastest adsorption dynamics. Thus, it can be concluded that for smaller particle size, the adsorption dynamics is limited predominantly by flow resistance whereas for larger particles it is the combination of thermal diffusion through the bed and intra-particle mass diffusion which governs the adsorption dynamics. Fig. 8 also depicts that the adsorption dynamics for 30 µm particle is generally faster than 70 µm owing to faster kinetics except for domain I. Revisiting the equation for critical aspect ratio (Eq. (13)) for 70 µm particle size yields a numerical value of 9 and hence, the inequality equation is satisfied by all the domains considered in this study. On the contrary, for 30 µm particle size domain I does not satisfy the inequality condition and shows the anomalous behavior. This further emphasizes on the adverse effect of pressure drop on adsorption dynamics. Thus, during the design of adsorption heat exchanger, one may use inequality Eq. (13) as a guiding principle to optimize the fin height to its pitch ratio.
4.3 Specific cooling capacity The main objective to study the adsorber domain is to predict the cooling capacity based on the adsorption dynamics. Theoretical specific cooling capacity (SCC) for each domain can be estimated by the following mathematical relationship: SCC
0.8 II I h fg t0.8
(14)
Here, II I represents the maximum uptake by the domain. Any adsorption system will take infinitely long time to achieve the saturation uptake of II ; hence, practical adsorption chillers operate with a finite cycle time. In this paper, 80% of maximum uptake is adopted to determine the adsorption cycle time t0.8 as in done in many previous studies . Table 2 shows the SCC for the selected domains and the particle size considered in this study. The CFD study shows that for the present operating conditions and heat exchanger geometry, the SCC ranges between 424 and 710 W/kg. It can be observed that the maximum cooling capacity with 30 μm particle size can be obtained using domain III whereas domain I is best suited for 70 μm particles. For smaller particle size, uptake is limited by flow resistance hence, a domain with smaller height is preferable; whereas adsorber with larger particle size is limited by thermal transport thereby requiring a domain with larger heat transfer surface. Therefore, it can be concluded that the optimum heat exchanger geometry is dependent on the particle size chosen. Further, it must be noted that the trend for cooling capacity closely imitates the adsorption dynamics seen in Fig. 8.
4.4 Comparison with lumped model Even though a 2-dimensional rigorous CFD model is essential to predict the adsorption dynamics of a practical chiller, the intensive computational requirement limits its utilization. Majority of the studies still use the lumped model to predict adsorption dynamics where the spatial variation of pressure and temperature are neglected for computational simplification. In other words, the heat exchanging domain is assumed to be near isobaric and isothermal. In this scenario, one can predict the temporal variation of uptake by merely integrating the LDF equation (Eq.(2)) which yields an exponential function:
1 e
t
(15)
Where the normalized uptake is represented as:
I II I
(16)
Similarly, the normalized average uptake
for each domain may be defined as:
I II I
(17)
Here, represents the spatial averaged uptake for each domain. Fig. 9 compares the normalized uptake predicted by the lumped LDF model calculated from Eq. (15) with average normalized uptake obtained from the CFD simulation results for each domain and particle size. The non-dimensional time
t is chosen for this comparison. The figure shows that
lumped LDF model over predicts the adsorption uptake for all configurations. This model incurs significant error for smaller particle size attributed to the large pressure drop that occurs in such situation and therefore the isobaric assumption is not valid. This deviation reduces as the particle size increases. Nevertheless, the marginal error for larger particle size occurs due to the nonisothermal nature of the domain. It can also be observed that the lumped model is more accurate in predicting the adsorption dynamics for smaller aspect ratio (wider domain). Thus, it can be concluded that the lumped LDF model may be used with reasonable accuracy for adsorption chillers with large adsorbent particle size and small aspect ratio.
5. Conclusion This paper investigates the presence of optimum heat exchanger geometry with respect to the adsorbent particle size elucidating the bottlenecks due to intra-particle mass diffusion, interparticle flow resistance and thermal transport. An adsorption system using ethanol and activated carbon (Maxsorb-III) is selected for this purpose. CFD study of a 2-dimensional configuration is employed to investigate the spatial variation of thermodynamic parameters within the domain. Three domains with the same area but different aspect ratios (2.25, 4 and 9) are considered along with two particle sizes (30 and 70 µm). The study indicates that based on the particle size and aspect ratio, certain domains are limited by vapor transport while others are limited by thermal and intra-particle mass diffusion. Further, it is shown that the use of smaller particle size does not
always lead to enhanced adsorption dynamics as the ratio of fin height to its pitch (aspect ratio) also plays an important role. The domain aspect ratio should remain lower than a critical value for maximizing the adsorption dynamics. Specific cooling capacity (SCC) derived from simulation results indicate the existence of optimum heat exchanging geometry for a particular particle size. Taller domain is preferable for larger particle size whereas wider domain is suitable for smaller particle size. The SCC calculated for the present study ranges between 424 to 710 W/kg of Maxsorb III. A comparison of CFD results with the lumped (isothermal and isobaric) model reveals significant deviation between the two. This deviation is minimum when the adsorbent particle size is large and a wide domain (small fin height to fin pitch ratio) is chosen for the adsorption process.
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Domain boundary
Vapour inlet
Fins
Symmetry Adsorbent bed
Y
Isothermal y walls
Tube surface
X
x Adsorber heat exchanging unit
Domain boundary conditions
Fig. 1: Adsorber domain boundary conditions
Uptake (kg kg-1 )
1.4
1.2
30°C 46.5°C
1.0
II
70°C
III
max
0.8 Tcold 0.6 0.4
I
IV Thot
Tads,i
0.2 pevap
pcond
0.0 1
2
3
4
5 6 7 Pressure (kPa)
8
9
Fig. 2: Operating and initial conditions on adsorption pressure-uptake plot
10
11
40 Simulation result
38
Temperature (ºC)
Experimental data 36 34 32 30 28 26 0
50
100
150 Time (s)
200
250
300
Fig. 3: Comparison of simulated temperature curve with experimental data [52] for ethanol adsorption onto activated carbon packed tube-fin assembly
a)
Domain I Pressure (kPa)
Domain II
Domain III
b)
Domain I Temperature ( C)
Domain II
Domain III
c)
Domain I Uptake (kg kg-1)
Domain II
Domain III
Fig. 4: a) Pressure b) temperature c) uptake contour plots at t = 10 s and dp = 30 µm
Fig. 5: Adsorption dynamics for various domains and dp = 30 µm
a)
b)
Fig. 6: Temporal plots of a) Pressure drop b) average domain temperature for dp = 30 µm
a)
b)
Fig. 7: Temporal plots comparing the a) pressure drop b) average domain temperature for 30 µm and 70 µm particle sizes
Fig. 8: Dynamics adsorption characteristics for various domains and particle size
Fig. 9: Comparison of normalized uptake obtained from lumped LDF model and as obtained from the present CFD study for various domains and particle sizes
Table 1: Numerical value of parameters used in this study Parameter
Value
Total surface area
3045 m2 g-1
Micro-pore volume
1.7 cm3 g-1
Average pore width
1.12 nm
Characteristic energy for D-A equation E
139.5 kJ kg-1 [54]
Maximum uptake max
1.2 kg kg-1
Heterogeneity parameter n
1.8
Activation energy Ea
225 kJ kg-1 [54]
Pre-exponential diffusion constant Ds
1.972×10-11 m2s-1
Specific heat capacity C p ,bed
0.82 kJ kg-1 K-1
Thermal conductivity keff
0.066 W m-1 K-1 [20]
Bed porosity
0.38
Packing density bed
290 kg m-3
Heat of adsorption hads
1002 kJ kg-1 [7]
Table 2: Specific cooling capacity for all the domains and particle sizes Specific Cooling Capacity (W/kg) Particle size (µm)
Domain I
Domain II
Domain III
30
424
682
710
70
517
493
445
Highlights
A 2-D transient study on adsorption dynamics of ethanol onto Maxsorb III is conducted.
Mass transfer limits adsorption dynamics in high aspect ratio heat exchanger geometry.
Heat transfer limits adsorption dynamics for small aspect ratio heat exchangers.
Higher aspect ratio is preferable for larger adsorbent particle size.
Lumped LDF model leads to erroneous results for smaller particles and high aspect ratio geometry.