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Experimental and numerical studies on the treatment of wet astronaut trash by forced-convection drying
Acta Astronautica 138 (2017) 384–393
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Experimental and numerical studies on the treatment of wet astronaut trash by forced-convection drying J.M.R. Apollo Arquiza a, *, Jean B. Hunter a, Robert Morrow b, Ross Remiker b a b
Cornell University, Ithaca, NY 14853, USA Sierra Nevada Corporation, Madison, WI 53717, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Astronaut trash Water recovery Mathematical modeling Drying Simulation
During long-term space missions, astronauts generate wet trash, including food containers with uneaten portions, moist hygiene wipes and wet paper towels. This waste produces two problems: the loss of water and the generation of odors and health hazards by microbial growth. These problems are solved by a closed-loop, forcedconvection, heat-pump drying system which stops microbial activity by both pasteurization and desiccation, and recovers water in a gravity-independent porous media condensing heat exchanger. A transient, pseudohomogeneous continuum model for the drying of wet ersatz trash was formulated for this system. The model is based on the conservation equations for energy and moisture applied to the air and solid phases and includes the unique trash characteristic of having both dry and wet solids. Experimentally determined heat and mass transfer coefficients, together with the moisture sorption equilibrium relationship for the wet material are used in the model. The resulting system of differential equations is solved by the finite-volume method as implemented by the commercial software COMSOL. Model simulations agreed well with experimental data under certain conditions. The validated model will be used in the optimization of the entire closed-loop system consisting of fan, air heater, dryer vessel, heat-pump condenser, and heat-recovery modules.
1. Introduction Like people on earth, astronauts living in space also produce garbage. This “space trash” is mostly used food and drink containers which may have unconsumed portions, dirty hygiene wipes and paper towels, plastic packaging, and paper [1]. The current treatment of space trash is storage and then disposal. During the Space Shuttle missions, which generally lasted less than 16 days, trash was compressed in small bags, wrapped with duct tape, and then returned to earth [2]. In the International Space Station (ISS), trash bags are stored and periodically removed by the Russian Progress spaceship or private American space cargo crafts. For manned missions to distant destinations, such as a rendezvous with an asteroid or future Mars landing, resource recovery and stabilization of trash will be critical for success. A four-person crew is estimated to discard 1 kg day 1 of water in their trash [3] and recovery of this water will reduce payload mass and associated lift costs. Microorganisms can colonize the wet trash, especially the food and hygiene wipes, and as the experience of Mir and ISS demonstrates, microbial growth may lead to the generation of odors, allergens, and potential health hazards [4, 5]. Drying of the space trash by hot-air forced-convection can stop
microbial activity by combined pasteurization and desiccation, with the water vapor produced recovered by a condenser. Our research group, together with Orbital Technologies Corp. (ORBITEC), studied a closed air-loop, dryer and condenser system for astronaut trash. The system consists of a blower, air heater, wet material vessel, a gravityindependent Porous Media Condensing Heat Exchanger (PMCHX), thermoelectric heat pump, and waste heat recovery module (Fig. 1). The process may be adapted for drying crew laundry, recovering water from water-reprocessing brines, and dehydrating food and biomass from future bioregenerative systems. Drying is extensively used in agricultural post-processing and in the food, pharmaceutical and chemical industries. Its importance is evident in the large number of publications on drying principles, models, and sample-specific data in the literature. Several books have been written on the topic [6–9] and there is a journal dedicated to it (Drying Technology, Taylor & Francis, Philadelphia, PA). The drying of astronaut cabin waste or any type of trash, however, has not been reported. Drying is an energyintensive process and becomes economical only for a high-value product, which trash is not. In long-term space missions, the water in the wet trash is valuable enough to justify recovery by drying, but energy efficiency is
* Corresponding author. Current address: School of Biological and Health Systems Engineering, Arizona State University, Tempe 85281, USA. E-mail address: [email protected] (J.M.R.A. Arquiza). http://dx.doi.org/10.1016/j.actaastro.2017.06.006 Received 5 August 2016; Accepted 9 June 2017 Available online 15 June 2017 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.
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trash drying component in that model. The experimental studies needed to obtain model parameters and data for validation were conducted in an open air-loop prototype constructed for research on the heat and mass transfer aspects of trash drying (Fig. 2). The prototype was designed in collaboration with and fabricated by ORBITEC. 2. Model development 2.1. Problem description The cylindrical dryer is represented by an axi-symmetric geometry (Fig. 3). The trash bed is modeled as porous media with large pores [10, 11]. It is assumed that a pseudo-homogeneous continuum model can be used for the system [12]. The control volume contains both solid and gas phases, each having a different temperature (two-temperature model). Wet and dry pieces of trash make up the solid phase while the gas is humid air. The walls of the cylindrical dryer are assumed to be perfectly insulated, making the temperatures and moisture contents of the solid and gas phases a function only of the distance from the bottom (1-D model, variation along the z-axis only).
Fig. 1. Schematic for the closed-loop drying system for space trash.
2.2. Model assumptions Simplifying assumptions were used in the model. The bed porosity and dry solid composition are assumed to be both space and time invariant (negligible shrinkage and settling). The physical and transport properties of the trash and humid air do not significantly change across the operating temperature range (25–60 C). Constant air velocity throughout the bed is assumed since: (1) expansion of the gas due to decrease in pressure is negligible (observed pressure drop between inlet and outlet air <10 mmHg), (2) the increase in mass flow from addition of water vapor to the gas stream was always less than 3.5% (10–80% humidity at 30 C), and (3) the maximum air temperature change, from the entering air temperature of 60 C to the cold bed temperature of 25 C, corresponds only to a 10% increase in air volume. Diffusion of water in the solid bed is assumed to be negligible. The wet and dry pieces in the trash are expected to have different temperatures during drying. Evaporation of water in the wet materials would keep their temperature near the wet-bulb temperature (≈25 C) while the dry components would approach that of the hot air passing
Fig. 2. Experimental set-up used for trash drying.
Fig. 3. Schematic of the axi-symmetric computational domain used in the model. The dryer is represented by a pseudo-homogeneous continuum model with two phases: gas and solid. The variables of interest are the temperature and moisture content in each phase.
still needed for maximum benefit. A computational model for the drying of space trash would guide the optimization of a drying system such as the closed-loop, forced convection process investigated by our research group. This paper presents the formulation and validation of the packed-bed
them. In most cases the dry pieces will be hotter than the wet ones, and though they are in contact with each other, the heat conduction between them is assumed to be negligible. This assumption is likely valid since loose packing of the trash (porosity ¼ 0.91) greatly reduces the area for heat transfer by conduction. 385
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Fig. 4. Summary of the model showing its components and their relationships. The subscripts are a for the gas phase and b for the solid phase.
2.3.1. Solid-phase equations Bed enthalpy balance
A diagram showing the components of the mathematical model is given in Fig. 4.
∂Tb ρs ð1 εÞ cd Xd þ cp Xp þ cw MXd ∂t ¼ m0 ΔHvap þ cv ðTa Tb Þ þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
2.3. Governing equations The equations for the model were derived from enthalpy and moisture mass balances on a differential volume within the dryer containing both the solid and gas phases [6]. The resulting four differential equations are given below. These are used to solve for the four unknowns: humidity ratio of the air (W), moisture content in the wet components of the bed, dry basis (M), air temperature (Ta), and bed temperature (Tb). Hunter and coworkers [1] have formulated an ersatz trash which is mostly wet hygiene wipes and plastic (70% by mass). In the model, the trash was further simplified by assuming that it consists only of wet wipes (subscript d) and plastic (subscript p), with the wipes representing all wet materials (e.g. hygiene wipes, moist food), and the plastic all dry materials (e.g. gloves, office paper). Liquids confined in closed or nearlyclosed drink bags were not considered in the model. The use of a single pseudohomogeneous solid phase precludes the reporting of the different temperatures of the wet and dry components of the trash. Instead, the model defines a “mean” bed temperature, Tb, which is related to that of the wet and dry materials by the following equation, for a basis of a unit mass of bone-dry trash solids:
Heat effects associated with evaporation
ρs ¼
convective transport in air
1 Xd ρd
þ ρpp X
ρs ð1 εÞXd
(3)
∂M ¼ m0 ∂t
(4)
where m0 is the volumetric evaporation rate in the dryer, kg water s1 m3, assumed to be equal to the convective mass transfer between the bed and air:
m0 ¼ km a0 Wsurface W
(5)
Wsurface is the moisture content of air in contact with the surface of the wet solids.
where ΔHsensible is the increase in sensible heat of the bed since the start of drying (when everything is at the same initial temperature), c is the specific heat capacity, X is the mass fraction (dry basis), and T is the temperature. The subscripts d, p, and w are for the bone-dry wipes, plastic and water, respectively. Since M decreases during drying, the relationship changes with time.
conduction in air
convective exchange between air and bed
where ρd and ρp are the densities of the dry wipes and plastic, respectively. Water mass balance in bed
(1)
∂Ta ∂ ∂T1 ∂Ta ka ¼ε ½ρa va ca þ ρa va cv W ∂z ∂t ∂z ∂z |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(2)
The average dry solids density (ρs) is computed using the following equation:
ΔHsensible ¼ cd Xd þ cp Xp þ cw MXd Tb ¼ ½cd Xd þ cw MXd Td þ cp Xp Tp
½ρa ca þ ρa cv Wε
ha0 ðTa Tb Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
2.3.2. Gas-phase equations Ga-phase enthalpy balance for unit area of bed
ha0 ðTa Tb Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} convective exchange between air and bed
386
(6)
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2.1% Kim wipes (Kimberly-Clark, Neenah, WI, USA), and 1.1% non-latex laboratory gloves. The calculated total moisture content of the ersatz trash is 0.375 g water g1 bone-dry solids but nearly all of this water is present in the wet wipes and dog food. Considering only the wet materials, their initial moisture content is 2.75 g water g1 bone-dry initiallywet solids. Ambient air heated to 60 C entered the bottom of the trash vessel, passed through the bed, and exited at the top. Three air superficial velocities were used: 1.2, 2.2, and 3.1 cm s1 (380, 690, and 970 ml s1, respectively). Humidity probes (Hygrotron model, Hygrometrix, Alpine, CA, USA) and thermocouple probes (type J) were placed at the inlet and outlet of the dryer to measure the percent relative humidity (% RH) and temperature, respectively, of the air entering and leaving the system. An Agilent 34970A datalogger (Agilent Technologies, Santa Clara, CA, USA) automatically recorded the readings every 20 s. The difference between the exit and inlet air moisture contents was used to calculate the rate of drying. Each set of conditions were tested at least twice with good agreement between results.
All evaporation takes place only in the solid phase so there is no latent heat term for the enthalpy balance in the gas phase. Water vapor balance in gas
ερa
∂W ∂ ∂W ¼ ερa Dv þ m0 ∂t ∂z ∂z |{z} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} diffusion in air
evaporation
∂W ρa va ∂zffl} |fflfflfflffl{zfflfflffl
(7)
convective transport in air
2.4. Boundary and initial conditions The boundaries for the system are shown in Fig. 3. For the solid-phase equations, all of these have conditions of flux ¼ 0. The gas-phase equations also have zero flux conditions for the top, left and right boundaries. The bottom boundary is the air inlet temperature (Ta ≈ 60 C) and entering humidity ratio for Equations (5) and (6), respectively. For the initial conditions, the solid phase has M (z, 0) ¼ 2.75 g water (g bone-dry initially-wet solids) 1 and Tb (z, 0) ¼ 25 C. The gas phase is set to Ta (z, 0) ¼ 25 C and W(z,0) equal to the actual humidity ratio of the inlet air during the run (0.0015–0.003 kg water kg1 dry air).
3.2. Determination of heat and mass transfer coefficients with transfer area
2.5. Numerical solution
The model requires values for the heat and mass transfer coefficients for trash drying. Correlations for h and k can be found in the literature but these are for agricultural crops and regularly-shaped catalyst pellets which would not be suitable for the ersatz trash [15]. Moreover, the folding and packing of trash pieces in the bed makes the effective transfer area between the solids and air, A, difficult to estimate or measure. Drying experiments were therefore performed to determine the product of the transfer coefficients and area (hA and kmA) suitable to our system, using a thin-layer approach typically used for agricultural materials [6]. Single layers of wet-wipes and plastic pieces were used in the drying studies, and the kmA is given by the mass-transfer design equation:
Equations (2), (4), (6) and (7) were solved simultaneously using a commercially available finite element software, COMSOL Multiphysics (COMSOL Inc., Burlington, MA). The axi-symmetric computational domain is 0.27 m 0.1 m, with a mesh having 350 4 quadrilateral elements. The model simulation gave temperature and moisture content values of the solid and gas phases within the dryer at a given time. 2.6. Input parameters The input parameters used in the simulations are given in Table 1.
m ¼ km A Wsurface W
3. Experimental methods 3.1. Deep bed trash drying runs
(8)
where m is the rate of evaporation, km is the mass transfer coefficient, A is the total transfer area for the layer, Wsurface is the humid ratio of air on the surface of the wet solids, and W is the bulk humid ratio of air. The kmA can therefore be calculated if m, Wsurface, and W are known. In the single-layer drying runs, the sample mass was measured at regular time intervals (at least 5 min) until it became constant. The resulting drying curves had initial linear portions which were taken as the constant-rate periods. The % RH of the air entering the dryer was monitored with a humidity probe. Thermocouples were attached to the surface of the wet wipes and just below the single layer to measure the temperatures of the wet wipes and entering air, respectively. During the constant-rate period, the air inlet and wet wipes temperatures stayed fixed but at different values, further indicating steady-state conditions. It
Drying experiments using ersatz trash were performed on the system shown in Fig. 2. The cylindrical drying chamber (height ¼ 30.5 cm, diameter ¼ 20 cm) was insulated with 10 cm of polystyrene foam. For each run, the dryer was loaded with 690 g of ersatz trash which had an uncompressed bed height of about 27 cm. The trash formulation was taken from Ref. [1], with composition by mass of 42.3% plastic pieces (high density polyethylene, 10 mil thickness), 26.6% baby wet wipes (moisture content adjusted to 73%, wet basis) (Huggies All-Natural, Kimberly-Clark, Neenah, WI, USA), 12.4% office paper, 10% dog food (food scrap simulant, moisture content adjusted to 73%, wet basis) (Science Diet, Hill's Pet Nutrition, Inc., Topeka, KS, USA), 5.3% duct tape,
Table 1 Input parameters for the model. Parameter Density Air Dry wipes (cotton) Plastic (HDPE) Specific heat capacity Air Dry wipes (cotton) Plastic (HDPE) Water vapor Water Diffusivity of water vapor in air Thermal conductivity of air Bed height Porosity
Symbol
Value
Units
Source
ρa ρd ρp
Ideal gas 1500 960
kg m3 kg m3 kg m3
[13] [14]
ca cd cp cv cw Dv ka z ε
1.0 1.3 2.2 1.88 4.186 2.81 105 28.5 0.27 0.91
kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 m2 s1 kJ m1 s1 K1 m m3 voids m3
[13] [13] [13] [13] [13] [13] [13] This study This study
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and equal distribution of these among 6 single layers is 4 wipes in each. Therefore, the single-layer runs used wet-wipes in multiples of four with sufficient crumpled plastic pieces added to fill the layer (Table 2). The combinations with higher proportions of wet wipes were added to test the drying of trash with more wet materials. Air superficial velocities of 1.2, 2.2, and 3.1 cm s1 were used in the drying of single layers. At least two runs were done for each treatment level with excellent agreement among the replicates.
Table 2 Composition of single layers used in the experiment. Number of wet wipes
Number of plastic pieces
4 8 12
9 6 3
Mass fraction, dry basis wipes
plastic
0.176 0.390 0.658
0.824 0.610 0.342
4. Results and discussion was assumed that at this period, the air at the surface of the wet wipes has 100% RH, with its humid ratio (Wsurface) corresponding to the equilibrium vapor pressure at the wet wipes temperature. From the m, Wsurface, and W data, the kmA can be calculated by rearranging Equation (8)
km A ¼
m Wsurface W
4.1. Experimental heat and mass transfer coefficients with transfer area Fig. 5 shows the linear relationship of hA to the inlet air flowrate at 60 C. Each graph for the different wet wipes/plastic combinations (4 wet wipes/9 plastic, 8 wet wipes/6 plastic, 12 wet wipes/3 plastic) represents a constant transfer area, and as expected, the h becomes larger as the air flowrate increases [16]. The hA also increases with the number of wet wipes since the mass transfer area increases with more wet wipes. The resulting values for kmA are shown in Fig. 6. The effects of air flowrate and number of wet wipes on kmA are similar to that for hA.
(9)
The steady air inlet and wet-wipes temperatures throughout the constant-rate drying period indicates heat transfer to the bed only vaporizes water, and can be obtained from the evaporation rate:
q ¼ mHvap
(10)
4.2. Relationship of the gas interfacial water vapor concentration to moisture content of wet solid
The hot air transfers heat into the layer by convection:
q ¼ hA Tsurface Ta
(11) The water vapor concentration at the air-solid interface, Wsurface, can be calculated from Eq. (8):
The hA is calculated using the air and wet-wipe surface temperatures:
hA ¼
q Tsurface Ta
Wsurface ¼ W þ
(12)
m km A
(13)
Since the convective mass transfer for trash drying is mainly determined by the flow characteristics of the air [16], it is reasonable to assume that a drying run with unchanging inlet air conditions will have the same kmA throughout. For the single-layer experiments, the measured m, the kmA from the constant-drying period, and W of the air, was used in Eq. (13) to calculate Wsurface for a drying run. The moisture content of wet solid, M, was also obtained during drying. All the Wsurface and M data from the single-layer drying experiments are plotted in Fig. 7, with Wsurface converted to water activity defined as the ratio of actual partial pressure of water vapor to the equilibrium
Since the trash is about 70% by mass wet wipes and plastic, the ersatz trash was simplified by using only these materials. The plastic pieces were cut into rectangles of the same size as the wet wipes (19.5 by 17.7 cm) and both were crumpled into rough spheres. A single layer of crumpled plastic pieces and wet wipes is approximately 4.5 cm high. A load of ersatz trash in the deep-bed drying runs (Section 3.1) fills the drying chamber to around 27 cm height, suggesting that it can be approximated by 6 single layers of plastic pieces and wet wipes. A batch of ersatz trash for the deep-bed drying runs has 24 wet wipes
Fig. 5. The effect of air inlet superficial velocity on the heat transfer coefficient-area parameter (hA) for different wet-wipes plastic combination (60 C air temperature).
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Fig. 6. The effect of air inlet flowrate on the mass transfer coefficient-area parameter (kmA) for different wet-wipes plastic combination (60 C air temperature).
wet wipes). The graphs exhibit the typical pattern observed when biological products are dried in a deep bed; an initial constant-rate drying period (linear portion) followed by a falling-rate phase [6]. As expected, the trash dries faster with increasing air flow, since hA and kmA both increase with higher air velocities. The model simulations for air velocities of 2.2 and 3.1 cm s1 in Fig. 8 generally agree with the data, but underestimate the moisture contents when they fall below 0.50 g water per g1 of bone-dry initially-wet solids. This discrepancy is perhaps due to the difference in properties between the single-layer trash formulation (wet wipes-and-plastic only) used to determine the transfer coefficients and the ersatz trash in the deep bed drying runs. In particular, the dog food in the trash has a significant amount of moisture and its drying behavior may be different from that of the wet wipes. Fortunately, model discrepancies late in the run have little impact on the practical validity of the model. At a moisture content of
vapor pressure at the same temperature. The portions of the curve where the water-activity is 1 correspond to the constant-rate period. Polynomial fitting with EXCEL (Microsoft Corp., Redmond, WA, USA) was used to obtain an equation relating water activity to M for trash drying. 4.3. Model validation by comparing predicted drying curves for deep bed trash drying with experimental results We hypothesized that the ersatz trash load can be represented in the model by six layers of 4 wet wipes and 9 plastic pieces, one on top of the other. Simulations of the combined layers were done with COMSOL, and the experimental and computational drying curves are shown in Fig. 8 for the air superficial velocities used (1.2. 2.2 and 3.1 cm s1). The moisture content in the plots is all the water in the trash divided by the total bonedry masses of the trash components that were initially wet (dog food and
Fig. 7. The curve relating the gas interfacial water vapor concentration (expressed as water activity) with moisture content of wet wipes based on single-layer experiments. 389
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Fig. 8. Comparison of experimental and simulated deep bed drying curves for all the initially-wet pieces in the ersatz trash at air superficial velocities of: (a) 3.1 cm s1, (b) 2.2 cm s1, and (c) 1.2 cm s1. The discrepancies are discussed in the text.
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Fig. 9. Changes in the moisture content of the initially wet materials along the trash bed height at different times during drying. The top of the bed is at 0.27 m. The simulation used an air velocity of 2.2 cm s1 and model with 4 wet wipes/9 plastic pieces.
0.5 g water g1 bone-dry initially-wet solids, 81% of the water in the trash has been removed, and further drying becomes slower and ultimately more costly in terms of power. Moreover, the remaining water is insufficient to support microbial growth. Fig. 7 indicates that a moisture content of 0.5 g water g1 bone-dry initially-wet solids corresponds to a water activity <0.6, low enough for indefinite storage stability; while bacteria and molds can survive for long periods at low water activity, even the most xerophilic molds fail to grow below a water activity of 0.6 [17]. In contrast with the high flowrate runs, the simulation for 1.2 cm s1 in Fig. 8c gives lower moisture contents the entire drying run, indicating that it overestimates the drying rate. This result may be explained by channeling, where the air finds preferential paths as it goes through the bed [18]. Minimal drying will then be experienced by the sections that are bypassed by the air, decreasing the overall drying rate. We speculate that this phenomenon happens at slow air flows because the low pressure gradient across the dryer makes it difficult for the air to pass through the narrow spaces in the densely packed regions of the bed. Since channeling is not included in the model, the simulation would produce higher drying rates, resulting in bed moisture content values lower than those observed.
everywhere below this value after 8 h of drying. 4.5. Simulated evaporation-time profiles The closed-loop drying system will recover the water removed from the trash using a condenser, which will be designed based on the rate of evaporation from the bed. The model should reliably predict the water vapor production during drying at air velocities of 2.2 cm s1 and 3.1 cm s1, since simulation and experimental results agreed at these conditions. The effect of increasing the load of wet materials in the trash on the evaporation rate was also investigated by using the experimental transfer coefficients for the cases with 8 wet wipes/6 plastic pieces and 12 wet wipes/3 plastic pieces. The simulation results for velocities of 2.2 and 3.1 cm s1 are shown in Fig. 10a and b, respectively. For both flowrates, the maximum evaporation rates occur at the start of drying, when the largest driving forces for mass transfer are produced by the high initial moisture contents. The maximum evaporation rates also increase as the air moves faster through the bed. The curves for 8 wet wipes/6 plastic and 12 wet wipes/3 plastic show an initial constant evaporation rate of 0.61 g min1, and 0.81 g min1, respectively. In contrast, no constant evaporation rate period was observed for the 4 wet wipes/9 plastic simulations. We attribute this behavior to the small amount of wet material in the trash; the lower layers dry up quickly and enter the falling-rate period before significant evaporation has started at the upper sections. The dependence of the evaporation rate time-profile with air flowrate, as shown by the simulations, provides insight on the operation of the closed-loop drying system. At high flowrates, drying is faster but the condenser must handle large air volumes and condense water vapor rapidly. Low flow rates require less condenser capacity but extend the drying time. A computational model for the entire closed-loop drying system would be needed to optimize its design and operation.
4.4. Moisture contents along the bed height during drying from model To ensure that all wet materials in the trash have been dried enough to prevent microbial growth, moisture content values along the bed height should be known. This data would be tedious to obtain experimentally, since the trash near the top of the bed must be sampled at different times during the drying run. The model, however, can generate plots of moisture content along the bed height at any time. These are shown in Fig. 9 for the simulation of trash drying using an air velocity of 2.2 cm s1 and combination of 4 wet wipes/9 plastic pieces. Since the hot air contacts the lower layers first, it is expected that the moisture content at a given time would increase going from bottom to top, as confirmed by the graphs. The model can therefore show when to stop drying, based on the maximum allowable moisture content of the wet materials in the dried product. For example, if 0.5 g water g1 initially wet material is the desired minimum, Fig. 9 shows that the moisture contents are
5. Conclusions A porous media model has been developed for the forced-convection drying of a fixed bed of ersatz astronaut trash. The model represents the 391
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Fig. 10. Evaporation rates during drying calculated by the model for trash with varying proportions of wet to dry material at different air superficial velocities: (a) 2.2 cm s1 and (b) 3.1 cm s1.
energy cost per unit of recovered water under a range of operating conditions including air temperature, air flow rate, and initial moisture content of the trash. Off-nominal conditions, such as the presence of pools of liquid water in the crevices of the plastic, or water enclosed in impermeable beverage bags, are beyond the scope of this model. Performance optimization and estimation of power costs will also depend on other system conditions such as the heat and mass transfer coefficients of the condensers, condenser temperature, surface area, and the performance of the refrigeration system in the enthalpy recovery loop.
dryer as a pseudo-homogeneous continuum with two phases: gas and solid, each phase having a distinct temperature and moisture content. Transient differential equations containing these variables were solved numerically using a commercial finite volume element solver (COMSOL). Heat and mass transfer coefficients appropriate for trash drying, together with data for water vapor concentration at the gas-solid interface, were obtained experimentally and used as inputs to the model. The formulated model produces valid results for ersatz trash in the range of water recoveries of interest for an in-flight or planetary surface system for trash drying. Since all air flow through the system is by forced convection, and moisture in the trash moves only by evaporation and (to a small extent) capillary wicking, never by saturated flow, the drying process and its model are both completely gravityindependent. This drying model is the first component in a model of the entire system, intended for prediction of drying performance and
Acknowledgement We thank NASA for funding this work under STTR Phase I award OTC GS0144-FR-05-1 and Phase II award GS0180-TR-06-01.
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Nomenclature
ca cd cp cv cw Dv h ha' hA ΔHvap ka k ma kmA M m' m t Ta Tb va W Wsurface z ρa ρs ε μ
Heat capacity of air, kJ kg1 K1 Heat capacity of dry wipes (cotton), kJ kg1 K1 Heat capacity of plastic, kJ kg1 K1 Heat capacity of water vapor, kJ kg1 K1 Heat capacity of liquid water, kJ kg1 K1 Diffusivity of water vapor in, air m2 s2 Heat transfer coefficient, kJ s1 m2 K1 Volumetric heat transfer coefficient, kJ s1 m3 K1 Heat transfer coefficient*area, J min1 K1 Heat of vaporization of water, kJ kg1 Thermal conductivity of air, kJ s1 m1 K1 Volumetric mass transfer coefficient, kg s1 m3(kg water kg1 dry air) Mass transfer coefficient*area, g min1 (kg water kg1 dry air) Bed moisture content, dry basis, m3 voids m3system Volumetric evaporation rate, kg s1 m3 Total evaporation rate, kg s1 Time, s Air temperature, K Mean bed temperature, K superficial air velocity, m s1 Humidity ratio kg water, kg1 dry air Humidity ratio of air at solid surface, kg water kg1 dry air Bed height, m Density of air, kg m3 Density of dry solids, kg m3 Porosity, m3 voids m3system viscosity, kg s1 m1
[9] Ian Turner, A.S. Mujumdar (Eds.), Mathematical Modeling and Numerical Techniques in Drying Technology, Marcel Dekker, New York, 1997. [10] A.K. Datta, Porous media approaches to studying simultaneous heat and mass transfer in food processes. I: problem formulations, J. Food Eng. 80 (1) (2007) 80–95. [11] M.L. Hoang, P. Verboven, M. Baelmans, B.M. Nicolai, A continuum model for airflow, heat and mass transfer in bulk of chicory roots, Trans. ASAE 46 (2003) 1603–1611. [12] C.O. Castillo-Araiza, H. Jimenez-Islas, F. Lopez-Isunza, Heat-transfer studies in packed-bed catalytic reactors of low tube/particle diameter ratio, Ind. Eng. Chem. Res. 46 (23) (2007) 7426–7435. [13] Perry's Chemical Engineers' Handbook, 2008. Ed. Perry, R.H., 1924-1978. Green, D.W. eighth ed. McGraw-Hill, New York. [14] W.M. Haynes, D.R. Lide (Eds.), CRC Handbook of Chemistry and Physics: A ReadyReference Book of Chemical and Physical Data, 92nd ed, CRC Press, Boca Raton, FL, 2011. [15] M.K. Krokida, Z.B. Maroulis, D. Marinos-Kouris, Heat and mass transfer coefficients in drying: compilation of literature data, Dry. Technol. 20 (1) (2002) 1–18. [16] C.J. Geankoplis, Transport Processes and Separation Process Principles, fourth ed., Prentice Hall, Upper Saddle River, New Jersey, 2003. [17] A.D. Hocking, J.I. Pitt, Media and methods for detection and enumeration of microorganisms with consideration of water activity requirements, in: L.B. Rockland, L.R. Beuchat (Eds.), Water Activity: Theory and Applications to Food, Marcel Dekker, New York, 1987. [18] S. White, C. Tien, Analysis of flow channeling near the wall in packed-beds, Thermo Fluid Dynam. 21 (1987) 291–296.
References [1] J.B. Hunter, J.M.R.A. Arquiza, R. Morrow, W. Butrymowicz, Energy-efficient closed loop heat pump dryer FOR solid waste stabilization ON long duration space missions, in: 36th International Conference on Environmental Systems. Norfolk, VA, 2006. SAE Paper 2006-01-2088. [2] B.V. Peterson, M. Hummerick, M.S. Roberts, V. Krumins, A.L. Kish, J.L. Garland, S. Maxwell, A. Mills, Characterization of microbial and chemical composition of shuttle wet waste with permanent gas and volatile organic compound analyses, Adv. Space Res. 34 (2004) 1470–1476. [3] J.W. Fisher, J.A. Hogan, L. Delzeit, K. Wignarajah, R. Alba, G. Pace, T.A. Fox, Water recovery from wastes in space habitats - a comparative evaluation of SBIR prototypes, in: 39th International Conference on Environmental Systems. Savannah, GA, July 2009. SAE Technical Paper 2009-01-2342. [4] K. Makimura, et al., Fungal flora on board the mir-space station, identification by morphological features and ribosomal DNA sequences, Microbiol. Immunol. 45 (5) (2001) 357–363. [5] S.J. Vesper, W. Wong, C.M. Kuo, D.L. Pierson, Mold species in dust from the international space station identified and quantified by mold-specific quantitative PCR, Res. Microbiol. 159 (6) (2008) 432–435. [6] D.B. Brooker, F.W. Bakker-Arkema, C.W. Hall, Drying and Storage of Grains and Oilseeds, first ed., Van Nostrand Reinhold, New York, 1992. [7] S.J. Kowalski (Ed.), Drying of Porous Materials, Springer, London, 2007. [8] E. Tsotsas, A.S. Mujumdar (Eds.), Modern Drying Technology, Wiley-VCH, Weinheim, 2007.
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Contents lists available at ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
Experimental and numerical studies on the treatment of wet astronaut trash by forced-convection drying J.M.R. Apollo Arquiza a, *, Jean B. Hunter a, Robert Morrow b, Ross Remiker b a b
Cornell University, Ithaca, NY 14853, USA Sierra Nevada Corporation, Madison, WI 53717, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Astronaut trash Water recovery Mathematical modeling Drying Simulation
During long-term space missions, astronauts generate wet trash, including food containers with uneaten portions, moist hygiene wipes and wet paper towels. This waste produces two problems: the loss of water and the generation of odors and health hazards by microbial growth. These problems are solved by a closed-loop, forcedconvection, heat-pump drying system which stops microbial activity by both pasteurization and desiccation, and recovers water in a gravity-independent porous media condensing heat exchanger. A transient, pseudohomogeneous continuum model for the drying of wet ersatz trash was formulated for this system. The model is based on the conservation equations for energy and moisture applied to the air and solid phases and includes the unique trash characteristic of having both dry and wet solids. Experimentally determined heat and mass transfer coefficients, together with the moisture sorption equilibrium relationship for the wet material are used in the model. The resulting system of differential equations is solved by the finite-volume method as implemented by the commercial software COMSOL. Model simulations agreed well with experimental data under certain conditions. The validated model will be used in the optimization of the entire closed-loop system consisting of fan, air heater, dryer vessel, heat-pump condenser, and heat-recovery modules.
1. Introduction Like people on earth, astronauts living in space also produce garbage. This “space trash” is mostly used food and drink containers which may have unconsumed portions, dirty hygiene wipes and paper towels, plastic packaging, and paper [1]. The current treatment of space trash is storage and then disposal. During the Space Shuttle missions, which generally lasted less than 16 days, trash was compressed in small bags, wrapped with duct tape, and then returned to earth [2]. In the International Space Station (ISS), trash bags are stored and periodically removed by the Russian Progress spaceship or private American space cargo crafts. For manned missions to distant destinations, such as a rendezvous with an asteroid or future Mars landing, resource recovery and stabilization of trash will be critical for success. A four-person crew is estimated to discard 1 kg day 1 of water in their trash [3] and recovery of this water will reduce payload mass and associated lift costs. Microorganisms can colonize the wet trash, especially the food and hygiene wipes, and as the experience of Mir and ISS demonstrates, microbial growth may lead to the generation of odors, allergens, and potential health hazards [4, 5]. Drying of the space trash by hot-air forced-convection can stop
microbial activity by combined pasteurization and desiccation, with the water vapor produced recovered by a condenser. Our research group, together with Orbital Technologies Corp. (ORBITEC), studied a closed air-loop, dryer and condenser system for astronaut trash. The system consists of a blower, air heater, wet material vessel, a gravityindependent Porous Media Condensing Heat Exchanger (PMCHX), thermoelectric heat pump, and waste heat recovery module (Fig. 1). The process may be adapted for drying crew laundry, recovering water from water-reprocessing brines, and dehydrating food and biomass from future bioregenerative systems. Drying is extensively used in agricultural post-processing and in the food, pharmaceutical and chemical industries. Its importance is evident in the large number of publications on drying principles, models, and sample-specific data in the literature. Several books have been written on the topic [6–9] and there is a journal dedicated to it (Drying Technology, Taylor & Francis, Philadelphia, PA). The drying of astronaut cabin waste or any type of trash, however, has not been reported. Drying is an energyintensive process and becomes economical only for a high-value product, which trash is not. In long-term space missions, the water in the wet trash is valuable enough to justify recovery by drying, but energy efficiency is
* Corresponding author. Current address: School of Biological and Health Systems Engineering, Arizona State University, Tempe 85281, USA. E-mail address: [email protected] (J.M.R.A. Arquiza). http://dx.doi.org/10.1016/j.actaastro.2017.06.006 Received 5 August 2016; Accepted 9 June 2017 Available online 15 June 2017 0094-5765/© 2017 IAA. Published by Elsevier Ltd. All rights reserved.
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trash drying component in that model. The experimental studies needed to obtain model parameters and data for validation were conducted in an open air-loop prototype constructed for research on the heat and mass transfer aspects of trash drying (Fig. 2). The prototype was designed in collaboration with and fabricated by ORBITEC. 2. Model development 2.1. Problem description The cylindrical dryer is represented by an axi-symmetric geometry (Fig. 3). The trash bed is modeled as porous media with large pores [10, 11]. It is assumed that a pseudo-homogeneous continuum model can be used for the system [12]. The control volume contains both solid and gas phases, each having a different temperature (two-temperature model). Wet and dry pieces of trash make up the solid phase while the gas is humid air. The walls of the cylindrical dryer are assumed to be perfectly insulated, making the temperatures and moisture contents of the solid and gas phases a function only of the distance from the bottom (1-D model, variation along the z-axis only).
Fig. 1. Schematic for the closed-loop drying system for space trash.
2.2. Model assumptions Simplifying assumptions were used in the model. The bed porosity and dry solid composition are assumed to be both space and time invariant (negligible shrinkage and settling). The physical and transport properties of the trash and humid air do not significantly change across the operating temperature range (25–60 C). Constant air velocity throughout the bed is assumed since: (1) expansion of the gas due to decrease in pressure is negligible (observed pressure drop between inlet and outlet air <10 mmHg), (2) the increase in mass flow from addition of water vapor to the gas stream was always less than 3.5% (10–80% humidity at 30 C), and (3) the maximum air temperature change, from the entering air temperature of 60 C to the cold bed temperature of 25 C, corresponds only to a 10% increase in air volume. Diffusion of water in the solid bed is assumed to be negligible. The wet and dry pieces in the trash are expected to have different temperatures during drying. Evaporation of water in the wet materials would keep their temperature near the wet-bulb temperature (≈25 C) while the dry components would approach that of the hot air passing
Fig. 2. Experimental set-up used for trash drying.
Fig. 3. Schematic of the axi-symmetric computational domain used in the model. The dryer is represented by a pseudo-homogeneous continuum model with two phases: gas and solid. The variables of interest are the temperature and moisture content in each phase.
still needed for maximum benefit. A computational model for the drying of space trash would guide the optimization of a drying system such as the closed-loop, forced convection process investigated by our research group. This paper presents the formulation and validation of the packed-bed
them. In most cases the dry pieces will be hotter than the wet ones, and though they are in contact with each other, the heat conduction between them is assumed to be negligible. This assumption is likely valid since loose packing of the trash (porosity ¼ 0.91) greatly reduces the area for heat transfer by conduction. 385
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Fig. 4. Summary of the model showing its components and their relationships. The subscripts are a for the gas phase and b for the solid phase.
2.3.1. Solid-phase equations Bed enthalpy balance
A diagram showing the components of the mathematical model is given in Fig. 4.
∂Tb ρs ð1 εÞ cd Xd þ cp Xp þ cw MXd ∂t ¼ m0 ΔHvap þ cv ðTa Tb Þ þ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
2.3. Governing equations The equations for the model were derived from enthalpy and moisture mass balances on a differential volume within the dryer containing both the solid and gas phases [6]. The resulting four differential equations are given below. These are used to solve for the four unknowns: humidity ratio of the air (W), moisture content in the wet components of the bed, dry basis (M), air temperature (Ta), and bed temperature (Tb). Hunter and coworkers [1] have formulated an ersatz trash which is mostly wet hygiene wipes and plastic (70% by mass). In the model, the trash was further simplified by assuming that it consists only of wet wipes (subscript d) and plastic (subscript p), with the wipes representing all wet materials (e.g. hygiene wipes, moist food), and the plastic all dry materials (e.g. gloves, office paper). Liquids confined in closed or nearlyclosed drink bags were not considered in the model. The use of a single pseudohomogeneous solid phase precludes the reporting of the different temperatures of the wet and dry components of the trash. Instead, the model defines a “mean” bed temperature, Tb, which is related to that of the wet and dry materials by the following equation, for a basis of a unit mass of bone-dry trash solids:
Heat effects associated with evaporation
ρs ¼
convective transport in air
1 Xd ρd
þ ρpp X
ρs ð1 εÞXd
(3)
∂M ¼ m0 ∂t
(4)
where m0 is the volumetric evaporation rate in the dryer, kg water s1 m3, assumed to be equal to the convective mass transfer between the bed and air:
m0 ¼ km a0 Wsurface W
(5)
Wsurface is the moisture content of air in contact with the surface of the wet solids.
where ΔHsensible is the increase in sensible heat of the bed since the start of drying (when everything is at the same initial temperature), c is the specific heat capacity, X is the mass fraction (dry basis), and T is the temperature. The subscripts d, p, and w are for the bone-dry wipes, plastic and water, respectively. Since M decreases during drying, the relationship changes with time.
conduction in air
convective exchange between air and bed
where ρd and ρp are the densities of the dry wipes and plastic, respectively. Water mass balance in bed
(1)
∂Ta ∂ ∂T1 ∂Ta ka ¼ε ½ρa va ca þ ρa va cv W ∂z ∂t ∂z ∂z |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
(2)
The average dry solids density (ρs) is computed using the following equation:
ΔHsensible ¼ cd Xd þ cp Xp þ cw MXd Tb ¼ ½cd Xd þ cw MXd Td þ cp Xp Tp
½ρa ca þ ρa cv Wε
ha0 ðTa Tb Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
2.3.2. Gas-phase equations Ga-phase enthalpy balance for unit area of bed
ha0 ðTa Tb Þ |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} convective exchange between air and bed
386
(6)
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2.1% Kim wipes (Kimberly-Clark, Neenah, WI, USA), and 1.1% non-latex laboratory gloves. The calculated total moisture content of the ersatz trash is 0.375 g water g1 bone-dry solids but nearly all of this water is present in the wet wipes and dog food. Considering only the wet materials, their initial moisture content is 2.75 g water g1 bone-dry initiallywet solids. Ambient air heated to 60 C entered the bottom of the trash vessel, passed through the bed, and exited at the top. Three air superficial velocities were used: 1.2, 2.2, and 3.1 cm s1 (380, 690, and 970 ml s1, respectively). Humidity probes (Hygrotron model, Hygrometrix, Alpine, CA, USA) and thermocouple probes (type J) were placed at the inlet and outlet of the dryer to measure the percent relative humidity (% RH) and temperature, respectively, of the air entering and leaving the system. An Agilent 34970A datalogger (Agilent Technologies, Santa Clara, CA, USA) automatically recorded the readings every 20 s. The difference between the exit and inlet air moisture contents was used to calculate the rate of drying. Each set of conditions were tested at least twice with good agreement between results.
All evaporation takes place only in the solid phase so there is no latent heat term for the enthalpy balance in the gas phase. Water vapor balance in gas
ερa
∂W ∂ ∂W ¼ ερa Dv þ m0 ∂t ∂z ∂z |{z} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} diffusion in air
evaporation
∂W ρa va ∂zffl} |fflfflfflffl{zfflfflffl
(7)
convective transport in air
2.4. Boundary and initial conditions The boundaries for the system are shown in Fig. 3. For the solid-phase equations, all of these have conditions of flux ¼ 0. The gas-phase equations also have zero flux conditions for the top, left and right boundaries. The bottom boundary is the air inlet temperature (Ta ≈ 60 C) and entering humidity ratio for Equations (5) and (6), respectively. For the initial conditions, the solid phase has M (z, 0) ¼ 2.75 g water (g bone-dry initially-wet solids) 1 and Tb (z, 0) ¼ 25 C. The gas phase is set to Ta (z, 0) ¼ 25 C and W(z,0) equal to the actual humidity ratio of the inlet air during the run (0.0015–0.003 kg water kg1 dry air).
3.2. Determination of heat and mass transfer coefficients with transfer area
2.5. Numerical solution
The model requires values for the heat and mass transfer coefficients for trash drying. Correlations for h and k can be found in the literature but these are for agricultural crops and regularly-shaped catalyst pellets which would not be suitable for the ersatz trash [15]. Moreover, the folding and packing of trash pieces in the bed makes the effective transfer area between the solids and air, A, difficult to estimate or measure. Drying experiments were therefore performed to determine the product of the transfer coefficients and area (hA and kmA) suitable to our system, using a thin-layer approach typically used for agricultural materials [6]. Single layers of wet-wipes and plastic pieces were used in the drying studies, and the kmA is given by the mass-transfer design equation:
Equations (2), (4), (6) and (7) were solved simultaneously using a commercially available finite element software, COMSOL Multiphysics (COMSOL Inc., Burlington, MA). The axi-symmetric computational domain is 0.27 m 0.1 m, with a mesh having 350 4 quadrilateral elements. The model simulation gave temperature and moisture content values of the solid and gas phases within the dryer at a given time. 2.6. Input parameters The input parameters used in the simulations are given in Table 1.
m ¼ km A Wsurface W
3. Experimental methods 3.1. Deep bed trash drying runs
(8)
where m is the rate of evaporation, km is the mass transfer coefficient, A is the total transfer area for the layer, Wsurface is the humid ratio of air on the surface of the wet solids, and W is the bulk humid ratio of air. The kmA can therefore be calculated if m, Wsurface, and W are known. In the single-layer drying runs, the sample mass was measured at regular time intervals (at least 5 min) until it became constant. The resulting drying curves had initial linear portions which were taken as the constant-rate periods. The % RH of the air entering the dryer was monitored with a humidity probe. Thermocouples were attached to the surface of the wet wipes and just below the single layer to measure the temperatures of the wet wipes and entering air, respectively. During the constant-rate period, the air inlet and wet wipes temperatures stayed fixed but at different values, further indicating steady-state conditions. It
Drying experiments using ersatz trash were performed on the system shown in Fig. 2. The cylindrical drying chamber (height ¼ 30.5 cm, diameter ¼ 20 cm) was insulated with 10 cm of polystyrene foam. For each run, the dryer was loaded with 690 g of ersatz trash which had an uncompressed bed height of about 27 cm. The trash formulation was taken from Ref. [1], with composition by mass of 42.3% plastic pieces (high density polyethylene, 10 mil thickness), 26.6% baby wet wipes (moisture content adjusted to 73%, wet basis) (Huggies All-Natural, Kimberly-Clark, Neenah, WI, USA), 12.4% office paper, 10% dog food (food scrap simulant, moisture content adjusted to 73%, wet basis) (Science Diet, Hill's Pet Nutrition, Inc., Topeka, KS, USA), 5.3% duct tape,
Table 1 Input parameters for the model. Parameter Density Air Dry wipes (cotton) Plastic (HDPE) Specific heat capacity Air Dry wipes (cotton) Plastic (HDPE) Water vapor Water Diffusivity of water vapor in air Thermal conductivity of air Bed height Porosity
Symbol
Value
Units
Source
ρa ρd ρp
Ideal gas 1500 960
kg m3 kg m3 kg m3
[13] [14]
ca cd cp cv cw Dv ka z ε
1.0 1.3 2.2 1.88 4.186 2.81 105 28.5 0.27 0.91
kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 kJ kg1 K1 m2 s1 kJ m1 s1 K1 m m3 voids m3
[13] [13] [13] [13] [13] [13] [13] This study This study
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and equal distribution of these among 6 single layers is 4 wipes in each. Therefore, the single-layer runs used wet-wipes in multiples of four with sufficient crumpled plastic pieces added to fill the layer (Table 2). The combinations with higher proportions of wet wipes were added to test the drying of trash with more wet materials. Air superficial velocities of 1.2, 2.2, and 3.1 cm s1 were used in the drying of single layers. At least two runs were done for each treatment level with excellent agreement among the replicates.
Table 2 Composition of single layers used in the experiment. Number of wet wipes
Number of plastic pieces
4 8 12
9 6 3
Mass fraction, dry basis wipes
plastic
0.176 0.390 0.658
0.824 0.610 0.342
4. Results and discussion was assumed that at this period, the air at the surface of the wet wipes has 100% RH, with its humid ratio (Wsurface) corresponding to the equilibrium vapor pressure at the wet wipes temperature. From the m, Wsurface, and W data, the kmA can be calculated by rearranging Equation (8)
km A ¼
m Wsurface W
4.1. Experimental heat and mass transfer coefficients with transfer area Fig. 5 shows the linear relationship of hA to the inlet air flowrate at 60 C. Each graph for the different wet wipes/plastic combinations (4 wet wipes/9 plastic, 8 wet wipes/6 plastic, 12 wet wipes/3 plastic) represents a constant transfer area, and as expected, the h becomes larger as the air flowrate increases [16]. The hA also increases with the number of wet wipes since the mass transfer area increases with more wet wipes. The resulting values for kmA are shown in Fig. 6. The effects of air flowrate and number of wet wipes on kmA are similar to that for hA.
(9)
The steady air inlet and wet-wipes temperatures throughout the constant-rate drying period indicates heat transfer to the bed only vaporizes water, and can be obtained from the evaporation rate:
q ¼ mHvap
(10)
4.2. Relationship of the gas interfacial water vapor concentration to moisture content of wet solid
The hot air transfers heat into the layer by convection:
q ¼ hA Tsurface Ta
(11) The water vapor concentration at the air-solid interface, Wsurface, can be calculated from Eq. (8):
The hA is calculated using the air and wet-wipe surface temperatures:
hA ¼
q Tsurface Ta
Wsurface ¼ W þ
(12)
m km A
(13)
Since the convective mass transfer for trash drying is mainly determined by the flow characteristics of the air [16], it is reasonable to assume that a drying run with unchanging inlet air conditions will have the same kmA throughout. For the single-layer experiments, the measured m, the kmA from the constant-drying period, and W of the air, was used in Eq. (13) to calculate Wsurface for a drying run. The moisture content of wet solid, M, was also obtained during drying. All the Wsurface and M data from the single-layer drying experiments are plotted in Fig. 7, with Wsurface converted to water activity defined as the ratio of actual partial pressure of water vapor to the equilibrium
Since the trash is about 70% by mass wet wipes and plastic, the ersatz trash was simplified by using only these materials. The plastic pieces were cut into rectangles of the same size as the wet wipes (19.5 by 17.7 cm) and both were crumpled into rough spheres. A single layer of crumpled plastic pieces and wet wipes is approximately 4.5 cm high. A load of ersatz trash in the deep-bed drying runs (Section 3.1) fills the drying chamber to around 27 cm height, suggesting that it can be approximated by 6 single layers of plastic pieces and wet wipes. A batch of ersatz trash for the deep-bed drying runs has 24 wet wipes
Fig. 5. The effect of air inlet superficial velocity on the heat transfer coefficient-area parameter (hA) for different wet-wipes plastic combination (60 C air temperature).
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Fig. 6. The effect of air inlet flowrate on the mass transfer coefficient-area parameter (kmA) for different wet-wipes plastic combination (60 C air temperature).
wet wipes). The graphs exhibit the typical pattern observed when biological products are dried in a deep bed; an initial constant-rate drying period (linear portion) followed by a falling-rate phase [6]. As expected, the trash dries faster with increasing air flow, since hA and kmA both increase with higher air velocities. The model simulations for air velocities of 2.2 and 3.1 cm s1 in Fig. 8 generally agree with the data, but underestimate the moisture contents when they fall below 0.50 g water per g1 of bone-dry initially-wet solids. This discrepancy is perhaps due to the difference in properties between the single-layer trash formulation (wet wipes-and-plastic only) used to determine the transfer coefficients and the ersatz trash in the deep bed drying runs. In particular, the dog food in the trash has a significant amount of moisture and its drying behavior may be different from that of the wet wipes. Fortunately, model discrepancies late in the run have little impact on the practical validity of the model. At a moisture content of
vapor pressure at the same temperature. The portions of the curve where the water-activity is 1 correspond to the constant-rate period. Polynomial fitting with EXCEL (Microsoft Corp., Redmond, WA, USA) was used to obtain an equation relating water activity to M for trash drying. 4.3. Model validation by comparing predicted drying curves for deep bed trash drying with experimental results We hypothesized that the ersatz trash load can be represented in the model by six layers of 4 wet wipes and 9 plastic pieces, one on top of the other. Simulations of the combined layers were done with COMSOL, and the experimental and computational drying curves are shown in Fig. 8 for the air superficial velocities used (1.2. 2.2 and 3.1 cm s1). The moisture content in the plots is all the water in the trash divided by the total bonedry masses of the trash components that were initially wet (dog food and
Fig. 7. The curve relating the gas interfacial water vapor concentration (expressed as water activity) with moisture content of wet wipes based on single-layer experiments. 389
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Fig. 8. Comparison of experimental and simulated deep bed drying curves for all the initially-wet pieces in the ersatz trash at air superficial velocities of: (a) 3.1 cm s1, (b) 2.2 cm s1, and (c) 1.2 cm s1. The discrepancies are discussed in the text.
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Fig. 9. Changes in the moisture content of the initially wet materials along the trash bed height at different times during drying. The top of the bed is at 0.27 m. The simulation used an air velocity of 2.2 cm s1 and model with 4 wet wipes/9 plastic pieces.
0.5 g water g1 bone-dry initially-wet solids, 81% of the water in the trash has been removed, and further drying becomes slower and ultimately more costly in terms of power. Moreover, the remaining water is insufficient to support microbial growth. Fig. 7 indicates that a moisture content of 0.5 g water g1 bone-dry initially-wet solids corresponds to a water activity <0.6, low enough for indefinite storage stability; while bacteria and molds can survive for long periods at low water activity, even the most xerophilic molds fail to grow below a water activity of 0.6 [17]. In contrast with the high flowrate runs, the simulation for 1.2 cm s1 in Fig. 8c gives lower moisture contents the entire drying run, indicating that it overestimates the drying rate. This result may be explained by channeling, where the air finds preferential paths as it goes through the bed [18]. Minimal drying will then be experienced by the sections that are bypassed by the air, decreasing the overall drying rate. We speculate that this phenomenon happens at slow air flows because the low pressure gradient across the dryer makes it difficult for the air to pass through the narrow spaces in the densely packed regions of the bed. Since channeling is not included in the model, the simulation would produce higher drying rates, resulting in bed moisture content values lower than those observed.
everywhere below this value after 8 h of drying. 4.5. Simulated evaporation-time profiles The closed-loop drying system will recover the water removed from the trash using a condenser, which will be designed based on the rate of evaporation from the bed. The model should reliably predict the water vapor production during drying at air velocities of 2.2 cm s1 and 3.1 cm s1, since simulation and experimental results agreed at these conditions. The effect of increasing the load of wet materials in the trash on the evaporation rate was also investigated by using the experimental transfer coefficients for the cases with 8 wet wipes/6 plastic pieces and 12 wet wipes/3 plastic pieces. The simulation results for velocities of 2.2 and 3.1 cm s1 are shown in Fig. 10a and b, respectively. For both flowrates, the maximum evaporation rates occur at the start of drying, when the largest driving forces for mass transfer are produced by the high initial moisture contents. The maximum evaporation rates also increase as the air moves faster through the bed. The curves for 8 wet wipes/6 plastic and 12 wet wipes/3 plastic show an initial constant evaporation rate of 0.61 g min1, and 0.81 g min1, respectively. In contrast, no constant evaporation rate period was observed for the 4 wet wipes/9 plastic simulations. We attribute this behavior to the small amount of wet material in the trash; the lower layers dry up quickly and enter the falling-rate period before significant evaporation has started at the upper sections. The dependence of the evaporation rate time-profile with air flowrate, as shown by the simulations, provides insight on the operation of the closed-loop drying system. At high flowrates, drying is faster but the condenser must handle large air volumes and condense water vapor rapidly. Low flow rates require less condenser capacity but extend the drying time. A computational model for the entire closed-loop drying system would be needed to optimize its design and operation.
4.4. Moisture contents along the bed height during drying from model To ensure that all wet materials in the trash have been dried enough to prevent microbial growth, moisture content values along the bed height should be known. This data would be tedious to obtain experimentally, since the trash near the top of the bed must be sampled at different times during the drying run. The model, however, can generate plots of moisture content along the bed height at any time. These are shown in Fig. 9 for the simulation of trash drying using an air velocity of 2.2 cm s1 and combination of 4 wet wipes/9 plastic pieces. Since the hot air contacts the lower layers first, it is expected that the moisture content at a given time would increase going from bottom to top, as confirmed by the graphs. The model can therefore show when to stop drying, based on the maximum allowable moisture content of the wet materials in the dried product. For example, if 0.5 g water g1 initially wet material is the desired minimum, Fig. 9 shows that the moisture contents are
5. Conclusions A porous media model has been developed for the forced-convection drying of a fixed bed of ersatz astronaut trash. The model represents the 391
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Fig. 10. Evaporation rates during drying calculated by the model for trash with varying proportions of wet to dry material at different air superficial velocities: (a) 2.2 cm s1 and (b) 3.1 cm s1.
energy cost per unit of recovered water under a range of operating conditions including air temperature, air flow rate, and initial moisture content of the trash. Off-nominal conditions, such as the presence of pools of liquid water in the crevices of the plastic, or water enclosed in impermeable beverage bags, are beyond the scope of this model. Performance optimization and estimation of power costs will also depend on other system conditions such as the heat and mass transfer coefficients of the condensers, condenser temperature, surface area, and the performance of the refrigeration system in the enthalpy recovery loop.
dryer as a pseudo-homogeneous continuum with two phases: gas and solid, each phase having a distinct temperature and moisture content. Transient differential equations containing these variables were solved numerically using a commercial finite volume element solver (COMSOL). Heat and mass transfer coefficients appropriate for trash drying, together with data for water vapor concentration at the gas-solid interface, were obtained experimentally and used as inputs to the model. The formulated model produces valid results for ersatz trash in the range of water recoveries of interest for an in-flight or planetary surface system for trash drying. Since all air flow through the system is by forced convection, and moisture in the trash moves only by evaporation and (to a small extent) capillary wicking, never by saturated flow, the drying process and its model are both completely gravityindependent. This drying model is the first component in a model of the entire system, intended for prediction of drying performance and
Acknowledgement We thank NASA for funding this work under STTR Phase I award OTC GS0144-FR-05-1 and Phase II award GS0180-TR-06-01.
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Nomenclature
ca cd cp cv cw Dv h ha' hA ΔHvap ka k ma kmA M m' m t Ta Tb va W Wsurface z ρa ρs ε μ
Heat capacity of air, kJ kg1 K1 Heat capacity of dry wipes (cotton), kJ kg1 K1 Heat capacity of plastic, kJ kg1 K1 Heat capacity of water vapor, kJ kg1 K1 Heat capacity of liquid water, kJ kg1 K1 Diffusivity of water vapor in, air m2 s2 Heat transfer coefficient, kJ s1 m2 K1 Volumetric heat transfer coefficient, kJ s1 m3 K1 Heat transfer coefficient*area, J min1 K1 Heat of vaporization of water, kJ kg1 Thermal conductivity of air, kJ s1 m1 K1 Volumetric mass transfer coefficient, kg s1 m3(kg water kg1 dry air) Mass transfer coefficient*area, g min1 (kg water kg1 dry air) Bed moisture content, dry basis, m3 voids m3system Volumetric evaporation rate, kg s1 m3 Total evaporation rate, kg s1 Time, s Air temperature, K Mean bed temperature, K superficial air velocity, m s1 Humidity ratio kg water, kg1 dry air Humidity ratio of air at solid surface, kg water kg1 dry air Bed height, m Density of air, kg m3 Density of dry solids, kg m3 Porosity, m3 voids m3system viscosity, kg s1 m1
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