Computer Simulation and Modeling of CO 2 Removal Systems for Exploration

Transcription

1 45th July 2015, Bellevue, Washington ICES Computer Simulation and Modeling of CO 2 Removal Systems for Exploration Robert F. Coker 1, James Knox 2, Greg Schunk 3, and Carlos Gomez 4 NASA Marshall Space Flight Center, Huntsville, Alabama, 35812, USA The Atmosphere Revitalization Recovery and Environmental Monitoring (ARREM) project was initiated in September of 2011 as part of the Advanced Exploration Systems (AES) program. Under the ARREM project and the follow-on Life Support Systems Project (LSSP), testing of sub-scale and full-scale systems has been combined with multiphysics computer simulations for evaluation and optimization of subsystem approaches. In particular, this paper will describe the testing and 1-D modeling of the combined water desiccant and carbon dioxide sorbent subsystems of the carbon dioxide removal assembly (CDRA), as well as initial 3-D modeling and test validation approaches for vacuum desorption. The goal is a full system predictive model of CDRA to guide system optimization and development. Nomenclature ε = porosity in the sorbent bed ρ s = sorbent density, kg m -3 D pellets = mean diameter of sorbent pellets, m P = total gas pressure, Pa T h = temperature at heater controller location, K T min = lower heater set point temperature (turns on), K T max = upper heater set point temperature (turns off), K S new = heater switch toggle for this timestep S old = heater switch toggle for previous timestep k m = mass transfer coefficient, s -1 c ps0 = sorbent heat capacity at ambient temperature, J kg -1 K -1 k s = sorbent thermal conductivity, W m -1 K -1 NASA = National Aeronautics Space Administration ARREM = Atmosphere Revitalization Recovery and Environmental Monitoring AES = Advanced Exploration Systems CDRA = Carbon Dioxide Removal Assembly ISS = International Space Station 4BMS = Four Bed Molecular Sieve SG = Silica Gel LSSP = Life Support Systems Project SCFM = standard (1 atm, 0 ºC) cubic feet per minute CBT = Cylindrical Breakthrough Test LDF = linear driving force TC = thermo-couple HC = half-cyle ECLS = Environmental Control and Life-support Systems 1 Aerospace Engineer, Thermal and Mechanical Analysis Branch, Space Systems Dept./ES22. 2 Aerospace Engineer, Environmental Control and Life Support Development Branch, Space Systems Dept./ES62. 3 Aerospace Engineer, Thermal Analysis and Control Branch, Spacecraft and Vehicle Systems Dept./EV34. 4 Aerospace Engineer, Thermal Analysis and Control Branch, Spacecraft and Vehicle Systems Dept./EV34.

2 Figure 1. Schematic of the CDRA 4BMS. Air comes in from the cabin, has water vapor removed in a desiccant bed (orange), is cooled by the precooler (yellow), has CO 2 removed in a sorbent bed (green), gets water vapor put back in in the 2 nd desiccant bed, then is returned to the cabin. Meanwhile, the 2 nd sorbent bed is heated and evacuated to space. FCC BCC VC POIST PDE CMMS = Face-Centered Cubic = Body Centered Cubic = vacuum characterization = Performance and Operational Issues System Testbed = partial differential equation = cooperative multimolecular sorption I. Simulation of the Full System Predictive simulation tools are being developed to reduce the hardware testing requirements of the Atmosphere Revitalization Recovery and Environmental Monitoring (ARREM) program and the follow-on Life Support Systems Project (LSSP) as part of the National Aeronautics Space Administration s (NASA) Advanced Exploration Systems (AES) program 1,2. Although sub-scale testing is required to establish the predictive capability of the simulations, the much greater cost of extensive full-scale testing can be limited to that required for the confirmation of analytical design optimization studies. Once predicative capability is established, geometric reconfiguration of a model is usually straightforward. A predictive simulation capability provides improved understanding of complex processes since process conditions (temperature, pressure, concentrations, etc.) may be examined anywhere in the sorption column. Weaknesses in a prototype design can be readily identified and improvements tested via simulation. Finally, the predictive simulation provides a powerful tool for virtual troubleshooting of deployed flight hardware. Here, we discuss using the COMSOL Multiphysics code 3 to model in detail and predictively the combined water desiccant and carbon dioxide sorbent subsystems, together known as a 4 Bed Molecular Sieve (4BMS), of the Carbon Dioxide Removal Assembly (CDRA) as it presently operates on the International Space Station (ISS). Fig. 1 illustrates the operation of the ISS CDRA 4BMS. Cabin air is sent through a desiccant bed, where water vapor is adsorbed. Then a precooler and blower pre-condition the dry air and send it through a sorbent bed where CO 2 is removed. The dry and (nominally) CO 2-free air then goes through the second (desorbing) desiccant bed, where water vapor is added back to the air stream. This is then returned to the cabin. Meanwhile, the second sorbent bed has one end closed off and is heated, which releases the CO 2 from the bed. After a short (~10 min) air save mode 2

3 Figure 2. CDRA sorbent bed. There are 5-6 zeolite pellets (white) across each small channel. Heater strips (brown) are visible on the folded aluminum channel fin structures (grey). that recovers the bulk of the air trapped in the sorbent bed, this is then vented to space. Such a half-cycle (HC) is typically 155 minutes long. On the next HC, the valves are switched so that the two adsorbing beds become desorbing and vice versa. A. 1-D Full System Modeling Approach Adsorption in packed fixed beds of pelletized sorbents is presently the primary means of gas separation for atmosphere revitalization systems. For the bulk separation of CO 2 and H 2O, temperature changes due to the heat of adsorption are significant, requiring the simulation of the heat balance equations through the beds and the housing, as well as the equations for sorption processes and fluid flow. For columns with small tube diameter to pellet diameter ratios, as encountered in internally heated columns such as the CDRA sorbent beds, flow channeling along the column wall can have a strong influence on overall performance. In non-cylindrical flow, the influence is great enough to eventually necessitate the use of 3-D simulations. Here, with over fifty pellets per cylinder diameter for the desiccant beds, 1-D models have proven accurate enough for predictively driven system design 4,5. However, as shown in Fig. 2, the sorbent beds are not cylindrical and the heaters used to assist in CO 2 desorption make for a potentially complex multi-dimensional flow path. In practice though, it seems that the dry air flows fairly uniformly through the channels, so that, nonetheless, a 1-D approximation may be sufficient to capture the bulk behavior of the beds. At the present time, full 3-D models are prohibitive, so for a quick turn around to guide the design of the next generation CDRA, 1-D models will be used. 3

4 The 4BMS is modeled as a fully coupled system, with the calculated mass fractions output as a function of time from one bed used as the inlet boundary condition for the next bed in the flow path. As discussed elsewhere, the 1-D COMSOL model is calibrated to test data from simple cylindrical tests 4,5. Thus, there are no knobs to turn and the model should be purely predictive. However, the CDRA 4BMS uses heater-assisted vacuum desorption to desorb the CO 2 sorbent bed, so the Cylindrical Breakthrough Test (CBT) validation experiments are not applicable to the desorbing CO 2 bed. Thus, additional calibration testing is required for heater-assisted vacuum characterization of the various sorbents (see Section III. below). In addition, as described in Ref. 5, some physics terms that could be neglected in higher pressure systems needed to be included for this work. Since the sorbent bed channels are a small number of pellet diameters in size, the effective porosity due to wall channeling will be higher in a 1-D model than the equivalent model for the desiccant beds. 1-D models of the ISS CDRA 4BMS were constructed using the COMSOL Multiphysics code using their chemical transport, Darcy flow, and thermal transport modules to solve for concentrations, pressures, and temperatures, respectively. Each one of the four beds is modeled as a separate domain with its own physics nodes, boundary conditions, and solver settings. Within each of these domains, the temperature of the sorbent, gas, and surrounding can are determined through separate heat transfer nodes. Domain partial differential equation (PDE) nodes are used to solve for the local pellet loading. Only the glass bead and sorbent-containing parts of the beds, as illustrated in Fig. 3, are modeled. A constant porosity, ε, the known density of the sorbent, s, and the measured mean particle diameter of the sorbent pellets, D pellets, was used for each bed. The glass bead layers are treated in the same way as the sorbent layers, but with zero adsorption and desorption capacity for H 2O and CO 2. COMSOL does not have an explicit bang-bang heater capability, so a Global Equation node for each CO 2 sorbent bed was used. This uses the Previous Solution capability introduced in COMSOL 5.0 to solve the following nested logic equation to determine if heater power should be applied: S new = if(t h T max, 0, if(t h T min, 1, S old )) (1). The first value after the if-test is used if the test is true, while the second is used if it is false. If S = 1, the heater is on; if S = 0, it is off. The model temperature at the location of the sensor (5.1 from the adsorption effluent) used to control the heater is T h. The minimum and maximum heater set-point temperatures are T min =390 F and T max =400 F, respectively. There are two heater strings each of 480W, with only the first being used during the 10 minutes of air save mode. Figure 3. Idealized schematic of 4BMS model. Only the glass beads (red) and sorbents (orange, yellow, blue, and purple) are modeled. The inlet and outlet regions (green) and thin wire cloths (grey) are not modeled. 4

5 Unlike previous work 5 which focused exclusively on sorption of a single sorbate (H 2O or CO 2), to model the full CDRA 4BMS, both sorbates must be included simultaneously. However, accurate binary Toth isotherms do not exist over the pressure and temperature range required here. To a first approximation, the CO 2 sorbent beds do not see any H 2O, so a single CO 2 isotherm is all that is needed. Similarly, the silica gel (SG) in the desiccant beds will effectively ignore CO 2. Thus, the only sorbent that will sorb both sorbates is the 13X in the desiccant beds. The13X will adsorb CO 2 only if there is little or no H 2O present. To model this behavior, a linear scaling factor was applied to the calculated single CO 2 isotherm equilibrium loading, such that normal CO 2 loading occurs at 0 H 2O loading and no CO 2 loading will occur if the H 2O loading is above q max = 5.6 mol/kg. Other than this, both the transport and sorption of the two sorbates are treated independently. The solutions for temperature, concentration, and loading are the same as in Ref. 5, though the former two variables now use COMSOL modules rather than PDEs. In addition, the latter now uses a heat of adsorption that now depends on temperature and sorbate partial pressure 6. The total pressure is determined by solving Darcy s law using that COMSOL module with a source term. Darcy s law is a simplification of Eqn. 2 from Ref. 5, such that the second order Forscheimer drag term, the term with the gradient of the viscosity, and the momentum change due to pellet loading are dropped. In future work, these terms will be added back in if deemed significant. The effluent mass fractions of CO 2 and H 2O from a bed are used as the input to the next downstream bed. Due to the blower and pre-cooler, the influent pressure and temperature of the adsorbing sorbent bed are regulated and thus are very different from the effluent from the adsorbing desiccant bed; constant measured values are used for the adsorbing CO 2 influent pressure and temperature. For the influent of the desorbing desiccant bed, an 8% thermal energy loss is applied to the sorbent bed effluent temperature to mimic transport losses between the beds; this value was determined from Performance and Operational Issues System Testbed (POIST) tests 8. Further, a ramp over the 1 st second of the time-dependent calculations was needed to slowly increase the influent temperature or the sudden rise in temperature at the desorbing desiccant influent would cause COMSOL to crash. A similar ramp was needed at the influent of the adsorbing CO 2 bed as it rapidly cools from over 400 F to ~50 F. The Sorbead WS SG that serves as a guard bed against liquid water (see Fig. 2) has no H 2O loading calibration data from the CBT. Therefore a published cooperative multimolecular sorption (CMMS) model was used for the isotherm of that bed 7. The Toth parameters used for the 5A RK38, the 13X G544, and the SG B125 are the same as given in Table 1 of Ref. 5. The physical characteristics of the pellets used in the model are given in Table 1, along with the resulting mass (per bed) and model porosity; they are little changed from the values in Ref. 5. However, the porosity of the RK38 bed is significantly higher than the other beds due to the narrow square channels of the sorbent bed resulting in larger empty regions near the walls, so a modeled, rather than measured, value for a similar 5A zeolite, G522, is used (see Section II. below). Further, the porosity of the glass and RK38 beds are increased by another 15% (beyond what is listed in Table 1) to reflect the increased channeling in the sorbent bed being dominant in the 1-D Table 1. Model Properties of Pellets Packed in the CDRA 4BMS Sorbent s c ps0(@26 C) k s D pellets mass kg m -3 J kg -1 K -1 W m -1 K -1 mm g Glass beads /148/ A (RK38) X (Grace Grade 544) SG (Sorbead WS) SG (Sylobead B125) Table 2. COMSOL Mass Transfer Coefficients Sorbent/Sorbate System k m (s -1 ) SG Sylobead B125/H 2O SG Sorbead WS/H 2O X Grade 544/H 2O X Grade 544/CO A RK38/CO

6 model; this choice was arbitrary. Also, to account for the thermal mass of the fins (see Fig. 1) in the sorbent bed, the mass of the aluminum bed was tripled; obviously this is an ad hoc approach, since the fins are in fact thermally separate from the 3-D geometry of the sorbent can. Table 2 lists the mass transfer coefficients k m used in the model. Although the mass transfer coefficient used in the linear driving force (LDF) model is a free parameter, it is not expected to be sensitive to different test conditions, such as flow rates, vapor pressure, or temperatures. Thus, it is not adjusted in the work presented here. In fact, all model input parameters are determined from the CBT or other tests or models, so that the work presented here is entirely predictive of the CDRA 4BMS behavior. Some required inputs, such as total sorbent mass, degree of thermal insulation, and pressure drops across the beds, are not known for the ISS CDRA 4BMS ground test that is used here for validation. Thermal insulation was assumed to be similar to the CBT, so the same heat transfer coefficient of 0.1 W/m 2 /K was used. The pressure drops are only needed for the model initial conditions, so reasonable guesses were made and iterated upon for quicker convergence. The mass transfer of CO 2 on 13X is not well known; although this will be addressed in future work, here it is assumed it behaves as on 5A. Based on CBT modeling, a 50% and 20% scale factor was applied to the permeability and convective heat transfer coefficients, respectively, that were derived from empirical relationships. However, the heat Table 3. CDRA-4EU Baseline Nominal Inputs Half-cycle time Inlet temperature Inlet dewpoint 155 min 49 F 40 F Inlet CO % Flow rate Air save 20.4 SCFM 10 min Figure 4. Influent temperature and water dew point for adsorbing desiccant bed for the baseline dataset. In this test, there is little variation. These data are used as inlet boundary conditions in the model. 6

7 Figure 5. Total pressure for desorbing sorbent bed. The effect of air save mode can be seen. The minimum pressure used in the model, due to numerical issues, is 0.02 torr. Everything right of the bump is a fit Gaussian curve. transfer coefficient relationships are not valid at low pressures, so for the desorbing sorbent bed, a scale factor that goes as (1 atm/p) was applied to the calculated coefficient. Some inputs may vary significantly over time and/or from test to test, so they are taken from the actual test being validated. The adsorbing desiccant bed inlet temperature and H 2O partial pressure and the desorbing sorbent bed effluent pressure are time-dependent values take from the tests. Flow rate (corrected from standard flow using the local measured pressure and temperature but unadjusted for any subsampling flow), ambient temperature, system inlet CO 2 partial pressure, sorbent bed influent temperature, and influent total pressures are constant values taken from the tests. Given these inputs, the COMSOL model should completely predict the behavior of the CDRA 4BMS, within the limits of the 1-D simplification and inherent accuracy of the LDF model. For faster runtime as well as increased numerical stability, the initial conditions for the bed loadings are set to be close to the expected final results. B. 1-D Results The COMSOL results for the predicted and experimentally measured exit temperatures and partial pressures are shown in the following figures. The baseline test data discussed here were taken on March 10 th, 2015 at MSFC on the CDRA-4 Engineering Unit Testbed. The nominal baseline operating conditions are given in Table 3. The system converges fairly quickly; the data discussed here are taken from the 4 th half-cycle. The gas temperature and H 2O dew point as a function of time at the adsorbing desiccant bed influent from the baseline dataset are given in Fig. 4. Even though these measurements are taken upstream of the actual influent, with a valve and significant piping between the sensors and the bed, the data are used as-is in the COMSOL model. Fig. 5 shows the time-dependent total pressure boundary condition used during desorption of the sorbent bed. At low pressures, the total pressure measurements are inaccurate and thus they have been replaced with a Guassian fit to the data; the non-monotonic nature of the noise at low pressures in the original data caused COMSOL to crash, even using a floor pressure value. Similarly, the data sampling rate is not fast enough to capture the first ~30s of the pressure, 7

8 so a data point equivalent to the adsorbing inlet pressure (~15 psi) has been added; linear interpolation is assumed in COMSOL between points in time. The temperatures, for both the baseline dataset and the COMSOL model, at the axial location of the thermocouples (TCs) used to control the heaters in the sorbent bed are given in Fig. 6. TC1 and TC2 refer to the modeled adsorbing Figure 6. Temperatures at the heater TC locations in the sorbent beds. The model cools too quickly during adsorption but otherwise matches the data well. Figure 7. Temperatures at the influent and effluent of the desiccant beds. The model peaks too high and too quickly during desorption. The model cools slightly during adsorption, while the data remains flat with time. 8

9 and desorbing beds, respectively, and heater_a_s and heater_d_s refer to the baseline experimental data for the adsorbing and desorbing beds, respectively. It can be seen that the model cools during adsorption too quickly (cf., the red curve to the dark blue curve). During desorption, the model matches the data fairly well, particularly since the 1- D model is calibrated to the simpler cylindrical geometry of the CBT and includes the fins (see Fig. 1) in only the most ad hoc fashion. For the desiccant beds, the temperature results are shown in Fig. 7. The model temperature at the effluent of the desorbing desiccant bed (yellow curve) peaks earlier and more sharply than the baseline data (red curve). The model temperature at the effluent of the adsorbing desiccant bed (purple curve) peaks early and then tapers off, while the Figure 8. Dew points at the influent and effluent of the desiccant beds. The model peaks too high and too quickly during desorption. The model adsorbing effluent and desorbing influent are the same since the sorbent bed does not interact with the water. baseline data (green curve) slowly rises to a near constant value. However, it must be noted that none of the data measurements are actually at the influent or effluent of the beds, but further away, after various piping and valves. The dew points of the baseline test and the model are shown in Fig. 8. Again, the model (yellow curve) peaks too early during desorption and the asymptotic desorption dew point is higher than the data (red curve). These differences are all likely tied to the rapid drop in temperature seen in the model during adsorption of the sorbent bed (see red curve in Fig. 6), since this will in turn make the temperature of the gas the desorbing desiccant bed sees (black curve in Fig. 7) peak too early and fall too quickly, leaving more water in the bed than is seen in the data. In Figs. 7 and 8, the model and data values for the adsorbing influent are identical, as stated above. Fig. 9 show the carbon dioxide partial pressure at the desiccant bed influent and effluent. Note the baseline data only has CO 2 measurements at the CDRA 4BMS influent and effluent. The model matches the spike near the beginning of the HC due to the CO 2 being competitively driven off of the 13X in the desiccant bed; the related adsorption of the CO 2 by the 13X during the first ~30 minutes of a HC can be see in the model adsorbing effluent curve (light blue). The baseline data show partial breakthrough of the CO 2 at late times through the desiccant bed 9

10 Figure 9. Partial pressure carbon dioxide at the desiccant bed influent and effluent. The data (green) shows some CO 2 breakthrough, while the model (purple) does not. The model adsorption effluent (light blue cruve) illustrates the competitive uptake of CO 2 by the 13X at the start of a HC. (green curve) which the model (purple curve) qualitatively captures. The early high tempeatures shown in Fig. 6, as well as perhaps too low of a void fraction in the sorbent bed (which is taken from a simpler CBT-like geometry), could explain this. The small amount of CO 2 that gets to the influent of the desiccant bed at the beginning of the HC (yellow curve) is due to the tiny amount of residual air trapped at the closed end of the desorbing sorbent bed. The rise at the end of the HC reflects the fact the sorbent bed is fully breaking through. Thus, by the end of a HC, both the 5A and the 13X are nearly fully loaded with CO 2. C. Summary The 1-D COMSOL model shows great promise in predictively modeling the CDRA 4BMS, even with some admittedly ad hoc approaches to the 1-D modeling of a very 3-D system. With some further validation, it will be used as a virtual laboratory to explore optimization of the 4BMS sub-system on ISS. Clearly the actual system is not 1-D and further empirical work will be needed, particularly to model the non-cylindrical channels of the sorbent beds. II. Direct Simulation of a CDRA CO 2 Sorbent Bed Channel The development of a three dimensional packed bed thermal/fluid model in COMSOL v4.4 composed of a spherical pelletized sorbent inside of a representative ISS CDRA sorbent bed channel is presented in this section. The development of a custom algorithm for the generation of random distributions of spherical pellets inside arbitrary packed bed geometries is also presented. Preliminary results indicate that, while computationally expensive, large multi-dimensional direct simulations of reduced or truncated packed beds may be feasible to gain insight into internal physics including the impacts of bed porosity, heat transfer and dispersion. 10

11 The NASA AES sponsored LSSP is dedicated to the advancement and development of closed loop ECLS technologies pursuant to future crewed space exploration. A fundamental aspect of the effort is the development of test correlated math models of relevant ECLS technologies. A predictive analytical capability is essential to guide sizing and optimization of ECLS subsystem and system designs. The development of a three dimensional model for direct simulation of an individual CDRA sorbent bed channel to provide insight into bed porosity, heat transfer, dispersion and void fraction is discussed. An individual channel is sufficient due to the inherent symmetry in the bed. Earlier attempts to characterize desorption flow through a representative CDRA channel utilizing analog ordered FCC (Face-Centered Cubic) or BCC (Body Centered Cubic) crystalline structures proved too porous due to the inherent low tortuosity of the resulting flow paths. A simplified sphere packing algorithm has been developed to randomly place identical sized (or sampled from a random distribution) spheres inside a truncated CDRA sorbent bed channel. The algorithm produces random sphere packings for a CDRA sorbent channel on the order of 55% (45% void fraction). The algorithm is initialized with an over filled channel of spherical pellets (i.e. overlapping spheres) and, through an iterative bumping process, excess spheres are removed. A few additional spheres are added via a second pass to identify voids in the lattice large enough to contain a sphere. COMSOL modeling of CDRA desorption flows through the resulting channels produced by the random packing algorithm are provided. A. CDRA CO2 Sorbent Bed The CDRA (see figure 1) contains two pelletized adsorbent beds to remove CO 2 respired by the crew. Each CO 2 adsorbent bed is paired with an upstream desiccant bed to condition the inlet air (i.e. remove water vapor) prior to entry into the adsorbent bed. While one adsorbent bed is actively capturing CO 2 at near ambient pressure, the other is regenerated through applied heat and vacuum desorption. The heaters and associated fins form many small axial channels through the length of the adsorbent beds (which are approximately 7.8mm x 13.2mm in cross section). The CDRA sorbent bed channels are filled with spherical sorbent pellets such that each channel span may only contain 3-5 of the nominal 2.38mm diameter Zeolite 5A (Grace Davison 522) pellets across. The small channels facilitate heat transfer from embedded heaters and fins during CO 2 desorption. At this small pellet to channel diameter ratio, wall effects may be laterally felt deep into the channel domain and increased bed porosity near the wall may affect flow distribution, axial pressure drop, lateral heat transfer and sorbent performance. The phenomenon of an unbalanced flow next to the wall due to increased void fraction is known as channeling. Channeling may adversely affect performance with an uneven sorption throughout the domain (i.e. greater near the walls). An open end picture of a CDRA sorbent bed is provided in Fig. 2 with a detailed view of an individual channel in Fig. 10. The bed is constructed by stacking alternating layers of heaters with an open serpentine fin assembly. The voids created in the fin assembly are subsequently filled with the spherical shaped pellets. Figure 10. CDRA Channel Detailed. A cross section of the CDRA sorbent bed is shown with an individual channel highlighted. The channel cross section is approximately 0.5 x 0.3 inches and 18 inches in depth. B. Spherical Packing Algorithm A simplified sphere packing algorithm (as shown in Fig. 11) has been developed to randomly place identical sized (or sampled from a random distribution) spheres inside of a truncated CDRA sorbent bed channel. The algorithm produces random sphere packings on the order of 55% (45% void fraction). The algorithm is initialized with a random over filled channel of spherical pellets (i.e. overlapping spheres) and, through an iterative bumping process, excess spheres are removed. As shown in figure 11, two overlapping spheres are bumped such that a small clearance is created at the closest approach. The size of the clearance is governed by a relaxation factor which is applied to the sphere movements to accelerate convergence. Through empirical observation, a relaxation of has been found to work well in the CDRA channel model. A relaxation of 1.0 will produce spheres that touch at a tangent point after each 11

12 movement. An iteration is defined as a single pass through all of the spheres in the model to identify overlaps with other spheres or the boundary. The boundary conditions are defined as either reflecting or pass-thru. At least one pass through boundary is necessary to allow excess spheres to escape. For a reflecting boundary any overlapping sphere will be wholly bounced back into the domain while, conversely, an overlapping sphere will be completely bounced out of the domain for a pass-through boundary. After convergence is achieved, a few additional spheres may be added via a search algorithm to identify voids in the domain large enough to hold an individual sphere. Figure 11. Sphere Packing Algorithm. An illustration of the random sphere packing algorithm for uniform spherical pellets is shown for spheres inside the domain and spheres residing against a boundary. A typical convergence profile is shown in figure 12 where N is the total number of spheres in the domain and D is the distance between any two spheres. The domain may be packed with twice the number of spheres that will actually fit. The convergence criteria is a double summation through all the spheres in the doman that overlap or touch (i.e. D < (R 1+R 2)). As the convergence criteria approaches 1.0 then no spheres overlap and convergence is achieved. For the results shown below, the tolerance used to define convergence is 10-8 (i.e. 1.0-convergence). Convergence is initially rapid as many excess spheres are easily pushed out of the domain. Iterating to remove the last overlapping spheres may become slow at the end but convergence is almost always achieved via this method. 12

13 Figure 12. Convergence. Convergence of the bed packing algorithm in terms of a given criteria is shown against iteration. The algorithm converges rapidly at first as extra spheres are discarded from the domain. A truncated CDRA channel packing with a uniform distribution of 2.38mm diameter spheres is shown in figure 13. The spheres are colored according to height in the domain and the channel is 7.8mm x 13.2mm in cross section and truncated to be just 30mm tall. A top view of the initial overlapping random distribution of spherical pellets is shown on the left with two views of the final packing shown on the right. Looking down from the top, huge voids reveal spheres at many different heights despite many more spheres forced into the domain. Interestingly, the convergence produces a quasi regular pattern of spheres with little but the topmost layer revealed. For a rectangular shaped domain, a void will always exist in the corners for spherical pellets as shown in the final packing but voids along the side walls are lessened with the optimal packing. An isometric view of the entire domain is shown on the far right and the algorithm produces a packing efficiency of 57.2% (void fraction=42.8%) overall. 13

14 Figure 13. CDRA Channel Packings. Initial and final spherical bed packings are shown for a representative case. The final packing assumes a much more organized appearance. A contour map of the bed void fraction is shown in figure 14. The local fraction is determined by tracing a perpendicular path through the packed bed and determing the ratio of free to open space. As expected the voids in the corners are evident with varying degrees of open space throughout the rest of the lattice. The void fraction through a slice (middle) of the domain is taken to show the change from the walls to the interior of the domain. Figure 14. Void Fraction. A local void fraction over the height of the bed is computed for a cross section divided by 100 units in each direction. The greatest void fractions are observed in the corners and a profile is shown across the profile to show how the void fraction approaches unity near the wall. 14

15 C. Three Dimensional CDRA Channel Model An external CAD package was used to create a geometry composed of all the spheres (based on location and radius) generated by the packing algorithm. The resulting geometry was imported into COMSOL Multiphysics v4.4 where a Boolean operation (subtraction) of the spherical geometry from a solid rectangular block was used to generate the flow domain as shown in figure 15. Dirichlet boundary conditions for the inlet were specified by a prescribed velocity and temperature and the temperatures of the top and bottom surfaces of the channel were also set to constant values to model the thermostatically controlled heaters inside the CDRA sorbent bed. All remaining boundaries were specified as no-slip and insulated except for the exit where a Dirichlet pressure was prescribed. The initial conditions were specified as shown to model a desorption condition inside the bed. Figure 15. COMSOL Geometry and Boundary Conditions. A case representing thermal and vacuum desorption of the CDRA bed is run with the prescribed boundary conditions. The geometry is meshed in COMSOL to produce over 1.6 million tetrahedral elements as shown in figure 16. Due to convergence problems with the boundary layers and closely packed spheres, the COMSOL General Physics Mesh Calibration was employed instead of Fluid Dynamics. Future efforts will consider slightly reducing the sphere diameters to improve clearance and possibly use the Fluid Dynamics calibration. Even without boundary layer elements, grid convergence was demonstrated for this laminar low Reynolds number flow through a range of COMSOL mesh settings from Normal->Fine->Extra Fine. The COMSOL Laminar Flow (spf) and Heat Transfer in Fluids (ht) modules were used to model the flow through the channel using a stationary, segregated study profile. 15

16 Figure 16. COMSOL Model. The channel model is discretized into tetrahedral elements with the greatest density in the spaces between spherical pellets and between the pellets and bounding walls of the domain. D. 3-D Results Velocities inside the bed are shown through the Y-Z midplane slice provided in figure 17. Peak velocities greater than a factor of ten relative to the inlet velocity are shown in the interstitial spaces around the spherical pellets. Surface temperature profiles are shown in figure 18 for a cold flow entering the bed with the heaters surfaces at the prescribed setpoints. The thermal entrance length is short as the stationary results show a slow moving fluid significantly warming the pellets in less than half the length of the truncated channel. 16

17 Figure 17. Results: Velocity Profiles inside the Channel. Peak velocities (interstitial) in the gaps between pellets and between pellets and the wall are approximately 10x the superficial velocity. Figure 18. Results: Surface Temperature Distribution. Boundary conditions representing the CDRA sorbent bed heaters are applied to the top and bottom walls. The thermal entry length is approximately 1/3 the length of the channel. 17

18 E. Summary A representative ISS CDRA sorbent bed channel, truncated in length and containing a random distribution of uniform spherical pellets, is modeled in COMSOL v4.4 under conditions of vacuum assisted thermal desorption. Direct simulation of the truncated channel, with a random distribution of spherical pellets was discretized into over 1.6 million tetrahedral elements, is demonstrated to obtain velocity and temperature profiles. Convergence problems, ostensibly due to pellet clearance, necessitated a mesh without boundary layer elements but future efforts will consider slightly reducing the sphere diameters to improve clearance and possibly use the default COMSOL Fluid Dynamics mesh calibration with boundary layer elements. The development of a custom, yet simplified, algorithm for the generation of random distributions of spherical pellets inside arbitrary packed bed geometries is also demonstrated. The mesh generation algorithm will be used to consider bed packings with non-uniform (i.e. varying diameter) distributions of spherical pellets. Preliminary results indicate that, while computationally expensive, large multidimensional direct simulations of reduced or truncated packed beds may be feasible to gain insight into internal physics including the impacts of bed porosity, heat transfer and dispersion. III. Multi-Dimensional Adsorption Model of CO 2/H 2O Sorbent Bed The objective of this simulation effort is to develop and correlate a 2-D axisymmetric adsorption/desorption COMSOL model of the VC (Vacuum Characterization) test article in order to capture radial effects. As discussed in Section I. above, a 1-D COMSOL baseline model has been created to understand the multi-physics being used during the adsorption process. This 1-D model has been successful at predicting water vapor on silica gel and zeolites and has been correlated to experimental data. However, this model only captures axial effects such as velocity, H 2O and CO 2 concentration and temperature gradients. The 2-D axisymmetric model captures the physics due to channeling of the carrier gas near the walls of the sorbent bed and the radially dependent porosity due to packing. Figure 19. Vacuum Characterization Test Article. Isometric View 18

19 Figure 20. Vacuum Characterization Test Article. Side View A. Vacuum Characterization Test The primary interest of the VC test is to experimentally characterize the adsorption and vacuum desorption of CO 2 of a pelletized sorbent bed in a large diameter column. The VC test article is shown in Figures 19 and 20. The aluminum canister is 3 in diameter and approximately 8 long allowing for variable sorbent bed loads from 1 to 6 in length. A series of cylindrical breakthrough test using water vapor and nitrogen as the carrier gas were conducted previously on this test setup before any vacuum testing. The sorbent used was zeolite G522 5A. This experimental data was used to calibrate and produce a predictive 1-D COMSOL H 2O adsorption breakthrough model. This calibration will insure that the physics and assumptions are correct for the 2-D axisymmetric model. B. 2-D Axisymmetric Modeling Approach The 2-D COMSOL axisymmetric model is a simple cylindrical geometry that consists of the sorbent bed and aluminum canister. The COMSOL modules used to represent the test were transport of concentrated species to track the H 2O, two heat transfer in solids for the sorbent bed and the aluminum can temperatures, heat transfer in fluids for the gas temperature, and a PDE for the mass transfer physics of adsorption. The model also uses a built-in Brinkman porous media flow interface which accounts for fluid velocity and pressure gradients in both the radial and axial directions. Previous versions of the model utilized 1-D user defined PDE s for momentum and continuity which did not capture radial effects of the flow. This model also makes the assumption that there is a variable porosity in the radial direction and a slip condition at the wall of the aluminum can. The inlet and initial conditions are based on the VC test configuration. Figure 21 shows the boundary conditions of the model. This breakthrough model has a simulation time of 450 minutes. 19

20 Figure 21. COMSOL Geometry and Boundary Condition 20

21 Figure 22. COMSOL Geometry and Mesh Figure 22 shows the refined mesh that was manually created at the wall where the sorbent bed is in contact with the aluminum can. This was done to capture the channeling effect due to the variable porosity in the radial direction near the wall. C. 2-D Results The 2-D axisymmetric model results are compared to the 1-D baseline model and VC experiment in the following figures. The center line temperatures of the VC H 2O breakthrough test where taken using thermal couples from three locations: 1 into the bed, 3.25 (the middle of the bed), and 5.5 (near the outlet of the bed). Figure 23 compares the experimental temperatures to the 1-D simulation results. The experiential data is in dotted-dashed curves. The experimental temperatures are slightly higher compared to the 1-D model. The 2-D axisymmetric temperatures seen in figure 24 are almost identical to the 1-D results. 21

22 Figure 23. Transient 1-D temperatures at TC locations. The 1-D model temperatures are lower and cools slightly faster compared to test data Figure 24. Transient 2-D temperature comparison. The 2-D axisymmetric centerline temperatures are almost identical to the 1-D model. 22

23 The 1-D breakthrough curve is compared to the VC test data on figure 25. The S-shape curve of the H2O breakthrough curve does not match the simulation curve. The error within the shape of the curve is something that is still being investigated. This might affect simulations where multiple cycles are being analyzed, such as for the CDRA 4BMS. Figure 26 shows where the data points were taken for the 2-D axisymmetric model. Figure 27 shows the 2-D axisymmetric model with the centerline point and wall breakthrough. The porosity varies sharply near the wall for a packed bed with spherical pellets since the geometry of packing is interrupted there. As a result, the velocity profile inside the packed bed is severely distorted near the wall. This phenomenon is known as flow channeling. A channeling effect was added to the model by using an expression that varies the porosity and increases it exponentially as it reaches the wall. This wall channeling allows the column to break through much quicker at this point. This is based on a slip condition boundary condition. Figure 28 shows the high H 2O concentration on the wall of the column due to the wall channeling. Figure 25. Transient 1-D H2O breakthrough. The 1-D model compared to the VC H2O test data 23

24 Figure 26. COMSOL point location for 2-D axisymmetric model. These point were plotted and compared to VC H 2O breakthrough data and 1-D model Figure 27. Transient 2-D H2O breakthrough curve. The wall channeling causes the column to breakthrough faster at the wall. This is based on a slip condition boundary at the wall. 24

25 Figure 28. H2O Concentration and column temperatures at 30 seconds of the simulation. The wall channeling can be seen on the left column. Temperatures are in Kelvin D. Summary The 2-D axisymmetric adsorption model has been developed to find and understand 3-D radial effects that a 1-D model cannot capture. Understanding these effects can help establish predictive capabilities that can be used to modify 1-D models for improved test correlations. The 1-D COMSOL model shows promise in predicting column adsorption for the VC test article. The previous H 2O breakthrough CBT data 4 helped in calibrating the 1-D model and in the creation of the 2-D axisymmetric model. Complexity was added by adding a variable porosity in the radial direction to mimic the wall channeling effect. Future models will include a no-slip condition that will change the concentration levels at the wall. A CO 2 breakthrough and vacuum test will be conducted in the near future with its own correlated 1-D model. IV. CDRA 4BMS Modeling Conclusion The objective of this work was to establish a path towards a virtual CDRA 4BMS testbed capability at MSFC. A 1-D model shows promise for predicting the 4BMS in its entirely. A 2-D model is under work to illustrate the impact of wall channeling, particularly during vacuum desorption. A 3-D model has been developed which will be used to inform the complex heat exchange and flow path in the CDRA sorbent bed during desorption. Together, these tools will help decrease cost and turnaround time for developing the next generation life support systems. References 1 Perry, J. L., et, al., "Integrated Atmosphere Resource Recovery and Environmental Monitoring Technology Demonstration for Deep Space Exploration,". AIAA, San Diego, Knox, J.C., et. al., "Development of Carbon Dioxide Removal Systems for Advanced Exploration Systems," International Conference on Environmental Systems. AIAA, San Diego,

26 3 COMSOL, COMSOL Multiphysics, Coker, R., Knox, J.C., Gauto, H., and Gomez, C., " Full System Modeling and Validation of the Cardbon Dioxide Removal Assembly, 44 th, Tucson, ICES , Coker, R., and Knox, J.C., "Full System Modeling and Validation of the Cardbon Dioxide Removal Assembly, Boston COMSOL 2014 Conference, Davison Chemical Report: Davison Molecular Sieves Adsorption Equilibria, undated. 7 Dong, X.U., et. Al., CO2 Capture by Vacuum Swing Adsorption Using F200 and Sorbead WS as Protective Pre-layers, Separation Science and Engineering, 20(5) , Knox, J.C. Performance Enhancement, Power Reduction, and Other Flight Concerns - Testing of the CO2 Removal Assembly for ISS.. Denver: SAE;