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Sorbent, Sublimation, and Icing Modeling Methods:

Experimental Validation and Application to an Integrated

MTSA Subassembly Thermal Model

Chad E. Bower1, Sebastian A. Padilla

2, and Christie S. Iacomini

3

Paragon Space Development Corporation, Tucson, Arizona, 85714

and

Heather L. Paul4

NASA Johnson Space Center, Houston, Texas, 77058

This paper details the validation of modeling methods for the three core components of a

Metabolic heat regenerated Temperature Swing Adsorption (MTSA) subassembly, developed

for use in a Portable Life Support System (PLSS). The first core component in the

subassembly is a sorbent bed, used to capture and reject metabolically produced carbon

dioxide (CO2). The sorbent bed performance can be augmented with a temperature swing

driven by a liquid CO2 (LCO2) sublimation heat exchanger (SHX) for cooling the sorbent bed,

and a condensing, icing heat exchanger (CIHX) for warming the sorbent bed. As part of the

overall MTSA effort, scaled design validation test articles for each of these three components

have been independently tested in laboratory conditions. Previously described modeling

methodologies developed for implementation in Thermal Desktop® and SINDA/FLUINT are

reviewed and updated, their application in test article models outlined, and the results of those

model correlations relayed. Assessment of the applicability of each modeling methodology to

the challenge of simulating the response of the test articles and their extensibility to a full scale

integrated subassembly model is given.

These models and modeling methodologies capture simulation of several challenging and

novel physical phenomena in the Thermal Desktop and SINDA/FLUINT software suite. Novel

methodologies include CO2 adsorption front tracking and associated thermal response in the

sorbent bed, heat transfer associated with sublimation of entrained solid CO2 in the SHX, and

water mass transfer in the form of ice as low as 210 K in the CIHX.

1 Sr. Thermal Analyst, 3481 E. Michigan Street Tucson, Arizona, 85714.

2 MTSA Project Lead, 3481 E. Michigan Street Tucson, Arizona, 85714.

3 Principal Investigator and Director of R&D, 3481 E. Michigan Street Tucson, Arizona, 85714, Senior AIAA

Member. 4 Space Suit PLSS Engineer, Space Suit and Crew Survival Systems Branch, Crew

and Thermal Systems Division, 2101 NASA Parkway, Houston, Texas, Mail code EC5.

41st International Conference on Environmental Systems17 - 21 July 2011, Portland, Oregon

AIAA 2011-5245

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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Nomenclature

Amod = CIHX model surface area

b1 = empirical constant

b2 = empirical constant

C3 = local adsorption efficiency factor

Cp = Specific heat at a constant pressure

dh = hydraulic diameter

hv = volumetric heat transfer coefficient

hc = surface convection heat transfer coefficient

kf = fluid thermal conductivity

m = mass

m& = mass flow rate

Mfrac = mass capacity fraction, ratio of stored CO2 to storage capacity

Minit = initial mass capacity fraction

Nu = Nusselt number

P = pressure

q& = heat flow rate

R = individual gas constant

Re = Reynolds number

T = temperature

t = time

X = flow mass fraction

η = efficiency

ρ = density

Subscripts:

Al = aluminum

article = of the test article

bed = of the sorbent bed

bulk = bulk or free stream

CO2 = carbon dioxide

d = based on hydraulic diameter

env = of environment

final = final condition

gas = of a reference gas

in = inlet condition

init = initial condition

latent = due to phase change enthalpy

lump = in a Thermal Desktop Lump

max = maximum

N2 = Nitrogen

out = outlet condition

passive = due to passive heat transfer

sensible = due to sensible energy change in the flow

tank = of the liquid in the CO2 storage tank

total = sum of flow constituents

wall = at wall

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I. Metabolic Heat Regenerated Temperature Swing Adsorption System Overview

Metabolic heat regenerated temperature swing adsorption (MTSA) that is incorporated into a Portable Life

Support System (PLSS) is being developed to remove and reject carbon dioxide (CO2) from the spacesuit ventilation

loop. Several studies explored the concept.1-3

A

schematic of the proposed system is shown in

Figure 1, and a brief explanation is provided here.

Expired CO2 in the ventilation loop is passed

through and selectively collected by a molecular

sieve consisting of 13X sorbent, also known as NaX

zeolite. The ability of NaX sorbent to adsorb CO2

increases with increasing partial pressure and

decreasing temperatures, and likewise decreases with

decreasing partial pressure and increasing temperature.

In the MTSA cycle, CO2 loading occurs at a

relatively low temperature and/or CO2 ventilation loop

partial pressure. The metabolic CO2 is rejected by an

increase in the bed temperature and / or exposure to

ambient pressure. This functionality is diagramed

for Mars and lunar operation in Figure 2. For

Martian operation, a temperature swing is required

since the partial pressure of CO2 in the vent loop is

similar to the pressure of the Martian environment.

The temperature swing is achieved by alternating

use of a liquid carbon dioxide (LCO2) sublimation

heat exchanger (SHX) for cooling the adsorbing bed

(to as low as 210 K) and a condensing icing heat exchanger (CIHX) that uses the energy present in the warm, moist

ventilation loop exhaust for warming the desorbing bed (up to ~280 K). On the moon, the lunar vacuum may provide

adequate pressure (or vacuum) swing alone to achieve sorbent regeneration. To provide continuous adsorption of CO2

from the PLSS ventilation loop, the technology relies on two separate beds that cycle to drive CO2 adsorption and

desorption.

Modeling challenges in simulating this system and proposed methodologies employing Thermal Desktop® have

been previously reported.4 The intent of the current paper is to show how these methodologies have been updated

and implemented into Thermal Desktop models. It also gives details pertaining to the exercise of these models in

simulation and operation of test articles previously built and used to demonstrate the feasibility of each of the three

Figure 1. Schematic Illustrating Two-bed MTSA

Subsystem Operation.

Figure 2. Two Bed Cycles to Regenerate the Sorbent Bed; (Left) Staging of Cycles; (Right) Temperature

and/or Pressure Swing.

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subsystems of the MTSA subassembly (the sorbent bed, the SHX, and the CIHX).1-3

It should be noted that these

test articles were designed based on the existing requirements and technology as understood at the time. The intent

was to build and test to-scale versions of the subcomponents, and this was done based on prior preliminary designs

efforts. During these efforts and through follow on efforts, the requirements for the system have changed and the

understanding of the technology has improved. Thus, the previous test articles are no longer a to-scale

representation of the current understanding of the technology. In order to improve the integrated MTSA

subassembly thermal model prior to upcoming Engineering Development Unit (EDU) testing, it was decided to

make use of this previously collected data. While the individual test articles are no longer to-scale, their use

elucidates the trends that may be seen when testing the MTSA subassembly that is now being built.

The process of correlating these test article models is described, showing the validity of the modeling methods,

as well as underlining methodology capability and shortcomings. It also allows discussion of extending the use of

these methodologies to that of generalized use in a fully integrated MTSA subassembly model. Testing and

demonstration of operation of the three submodels in a combined MTSA subassembly unit over full cycles is

planned for a future effort.

II. Submodel Verification

A. Sorbent Bed

At the core of the operation of the MTSA system is the sorbent bed that removes CO2 from the ventilation

loop gas. The sorbent is wash coated on to an aluminum foam substrate to both minimize the flow resistance through

the sorbent and to provide good thermal connection to the heating and cooling heat exchangers. Figure 3 shows an

example substrate embedded into a test article

designed to demonstrate the performance of the

MTSA application in a PLSS-relevant scale and

geometry1. The test article was tested in full

cycles. Adsorption was tested at a fixed

temperature of ~210 K and ~0.8 kPa CO2 partial

pressure. Desorption was tested in a simulated

Mars atmosphere (0.8 kPa pure CO2) at ~280 K.

The simulated ventilation gas consisted of 200

mg/s (1.54 lbm/hr) of N2 and 10.5 mg/s

(0.083lbm/hr) of CO2 at a total pressure of 30 kPa.

Since this test, MTSA requirements have been

updated, and the allowable volume has increased.

The tested flow rate is 28% of the expected full

scale while the volume is only 4.3% of full scale.

In addition, the MTSA cycle is now intended to cool from ~280 K to ~210 K during the adsorption half cycle rather

than adsorbing at a fixed temperature. While the article is no longer at a PLSS relevant scale and exhibits differences

in adsorption characteristics, the collected data is sufficient to verify the developed Thermal Desktop framework

upon which these more complex adsorption mechanics will operate.

A view of the discretized sorbent bed as developed for the methodology description is shown in the left hand

side of Figure 4. Here a single inlet flow branches into several equal flow rate axial flow paths which pass through a

series of discretized volumes representing the sorbent bed. As in this representation, the test model is discretized in 5

sections wide and high across the sorbent bed, and 10 sections in the flow direction. In the right hand side of Figure

4 is a detailed view of the originally described heat and mass transfer and storage framework in a representative

discretized volume.4 As in the zoomed out view to the left, the primary through flow path is represented in red and

contains the resistance to bulk flow through the volume. This path is thermally connected via the green tie to the

volume’s solid thermal mass, which is shown in blue. CO2 mass transfer is handled by the light blue path. The path

connects the primary process flow to a tank which represents a CO2 mass storage potential. In addition to mass flow

to and from this tank, it handles the adsorption enthalpy of 931 kJ/kg. Since the CO2 mass is in intimate contact with

the sorbent bed, the storage tank is thermally shorted to the nodal mass by a tie with a large conductance.

Figure 3.Cut View of the Sorbent Bed Test Article Design

(Left) and Interior View with Aluminum Foam with

Proprietary Wash Coating By Precision Combustion, Inc.

Cross section size: 1.25” x 1.25”.

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Figure 4. Flow and Volumetric Discretization of the Test Article Sorbent Bed (Left) and the Supporting

Framework for Heat and Mass Transfer Within the Discretized Volumes (Right).

This methodology was implemented into the sorbent test article model and although it does provide the expected

results, it was found to take far too long to run a full length simulation. Originally, the CO2 storage tank in this

model was intended to only contain the equilibrium mass of CO2 in a discretized volume. The initial simulations

revealed that such a small amount of thermal mass results in the calculation of very small time steps in

SINDA/FLUINT which corresponded to long run times. To increase the thermal mass contained in the CO2 storage

lumps and to otherwise simplify the model, all of the nodal thermal mass in the sorbent and aluminum foam was

lumped into the CO2 storage tanks. This collection requires that the thermal mass of the aluminum and sorbent be

translated into a thermal mass of a gas via the equation:

gasgaspbedbedp mCmC ** ,, =

(1)

In the equation, Cp is specific heat and m is mass while the subscript bed denotes the composite property of the

bed materials, Aluminum and NaX sorbent, and gas is the properties of the reference gas that is loaded into the

lumps. The inputs for an 8000 series gas (ideal gas) in a SINDA/FLUINT lump are constituent, temperature, and

pressure. It is desirable for the lump to contain only the adsorbed amount of the CO2. Sorbent bed thermal mass can

be replaced by adding an equal amount of one of the other constituents available in the fluid model, in this case the

reference gas is Nitrogen (N2). An equivalent thermal mass flow rate of Nitrogen is used in place of Oxygen as used

in the actual PLSS to ensure safety during testing. Since the Nitrogen is modeled as an ideal gas in the model, and

with the presumption that the sorbent bed and the storage lump have equal volumes, Equation 1 can be combined

with the ideal gas law to yield an input value for lump pressure.

initNbed

Np

bedp

lump TRC

CP ***

2

2,

,ρ= (2)

In Equation 2, Plump is the pressure input to the lump, ρbed is the composite density of the sorbent bed (density of

sorbent + density of foam), RN2 is the individual gas constant for Nitrogen, 296.8 J/kg-K, and Tinit is the initial

temperature of the sorbent bed. To eliminate energy errors due to variation in the specific heat of N2 and aluminum,

Cp bed and Cp N2, are evaluated at the mean temperature of the cyclic temperature swing.

The primary challenges in modeling this test article pertain to modeling descriptions of mass and heat transfer.

Detailed modeling methodologies for numerical simulation of the adsorption process were detailed in a previous

work.4 In that paper, a simple methodology was presented that drives the local weight percentage of CO2 loading to

equilibrium in the presence of a CO2 laden flow. In this methodology, if any capacity for adsorption exists in a local

unit volume, the local CO2 flow is calculated and set to be removed to the storage lump by the equation:

32max,2 CXmm COtotalCO&& =

(3)

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where m& CO2, max is the removed mass flow of CO2 as determined by the product m& total, the local total mass flow of

CO2 entering the domain mass fraction, and XCO2 the CO2 to total mass ratio, and a local extraction efficiency, C3.

A value of C3 approaching 1.0 was intended be used to derate the local adsorption to ensure that only CO2 is

removed from the flow while maintaining an assumption of equilibrium between the local flow concentration and

sorbent bed weight loading. Later comparison of the CO2 breakthrough trends in the test displayed that this is an

inadequate model since there is a gradual breakthrough rather than a sudden rush of unadsorbed CO2. A simple

empirical model that more closely represents a true mass transfer equation for non-equilibrium scenarios like this is

one where the rate of adsorption is proportional to the amount of spare capacity. A method of scaling the mass flow

rate from the upper efficiency limit to zero at equilibrium was developed and implemented. This relationship is

given in Equation 4.

−

−+=

11

max,22

init

initfrac

COCOM

MMmm &&

(4)

In this Equation Mfrac is the ratio of the amount of stored CO2 to the equilibrium capacity, and Minit is the initial

value of Mfrac at the beginning of a cycle. Derivation of the equation with Minit was intended to maintain the meaning

of C3 as the local efficiency at startup. In application the value of C3 is empirically derived to allow the model to

match the breakthrough profile of the test and is affected by the number of discretizations in the model. This

methodology would require either updates to accept CO2 pressure and bed temperature variation of the sorbent bed

capacity or appropriate mass transfer relationships to allow use in a Martian atmosphere, but is sufficient in its

current form to show functionality of adsorbent mass transfer in a Thermal Desktop environment. Additional

improvements can be implemented as funding allows.

The results of this modeling methodology are shown in Figure 5a, and as compared to the previous equilibrium

methodology in Figure 5b. The smooth “s” shaped mass fraction curves are expected as upstream lumps begin to

reach capacity allowing the local CO2 mass fraction in the flow to increase and taper off to the inlet value as the

local capacity is filled. This response verifies the general operability of the developed modeling method.

Figure 5. Local CO2 Mass Fractions Using a.) Current Methodology and b.) Previous Methodology.

Conductive and convective heat transfer mechanisms are captured in the developed model. Bulk conduction in

the aluminum substrate is modeled with finite difference elements (blue volumes in Figure 4) as previously

documented.4 Convection heat transfer in the sorbent bed is also important in simulating the system response. This

heat transport mechanism is responsible for transferring heat between the inlet flow and the sorbent bed and

distributes energy associated with adsorption and bulk heating or cooling downstream from the adsorption site.

Volumetric heating is described much like the more common areal heating, in terms of a Nusselt number, Nud which

relates the volumetric heat coefficient hv to a characteristic pore diameter, dh and the fluid conductivity kf in the

form: 4

f

hvd

k

dhNu

2

=

(5)

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Empirically determined forms of the Nusselt number as a function of Reynolds number, Re, have been reported

for the aluminum foams used in the MTSA sorbent bed.5 The general form of these equations is given in Equation 6

where the constants b1 and b2 are functions of the foam porosity.

2Re1

b

dd bNu =

(6)

The b1 and b2 values for three densities of foam were reported as reproduced in Table 1. In the MTSA

application, 92% porous foam was used, thus an interpolation on the 80% and 95% data was performed to yield the

equation 610.0Re335.0 ddNu = . This correlation is used despite application outside the reported testing conditions.

Although the aluminum foam used in testing by Hwang4 was

manufactured by ERG, the same manufacturer that supplies foam

for the MTSA, the reported mean pore size in the foam testing

presented by Hwang was approximately 2.0 mm which is

approximately equivalent to 10 pores per inch (ppi) foam. This is

much larger than the mean pore size of 0.5 mm calculated for 40

ppi foam used in MTSA testing. Furthermore, the flow velocity

through the foam in the heat transfer tests by Hwang appears to

be higher than in our MTSA application. This is presumed since

the Reynolds numbers reported by Hwang are in the range of

1900 to 7800 whereas the MTSA tests are orders of magnitude

lower, on the order of 7 to 10. Despite this large difference in correlation inputs, other reporters (cited in the Hwang

paper) have shown a similar log-linear relationship over a range inclusive of both the results reported by Hwang and

the MTSA application, lending confidence to the large extrapolation. At 280 K, the resulting Nusselt number is 1.14

and the associated volumetric heat transfer coefficient is 63,000 W/m3-K. In the MTSA application, variation in the

given equation with respect to temperature is low, so the volumetric heat transfer equation is evaluated and applied

across the model at the average of inlet and outlet temperature.

CO2 outlet concentration results (in parts per million by volume, PPM) from the correlated model as well as

composite test results are given in Figure 6. The composite test data is an average of 9 test cycles where each cycle

consisted of equal adsorption and desorption times, and each had a similar outlet concentration profile. Change in

weight percent loading, the ratio of CO2 mass loaded to NaX sorbent mass, was calculated from these data sets for

the time period from the start of flow into the bed

to the point of 5000 PPM CO2 breakthrough.

These changes in weight load estimates have an

average value of 5.6%. The model was correlated

by varying two model inputs, the equilibrium

weight loading percentage (obtained from the

sorbent vendor or empirically) and a new

modeling variable, C3 (see Equation 3), the local

extraction efficiency. Increase or decrease of the

equilibrium efficiency shifts the model

breakthrough profile to the right or left,

respectively. Increase or decrease of the local

efficiency results in two effects. Increase of local

efficiency increases the outlet concentration at

early times and in general flattens the curve at

later times and vice versa. In the best fit correlated

model, an outlet concentration of 5000 PPM

occurs in both the test and model at 49 seconds

when the model has captured 6.0% weight percent

change in CO2. For this solution, a fixed equilibrium weight loading value of 7.5% was used as model input, and the

best fit value for C3 is 0.62. A fixed equilibrium value is appropriate in this test case since the inlet temperature and

pressures were held constant for the duration of the test. These results demonstrate that the developed framework

can be used to describe adsorption processes in Thermal Desktop and that simple empirically derived mass transfer

equations can be used to predict performance for known geometry and flow inputs. As noted above, the simple

empirical equations presented here have been considered sufficient for subassembly design but will require

Figure 6. Sorbent Bed Outlet CO2 Concentration and

Correlated Model Results.

Table 1. Constants for Use in Empirically

Derived Nusselt Number Equation.1

ε b1 b2

0.95 0.3248 0.601

0.80 0.376 0.64

0.70 0.1569 0.825

0.70+ 0.80 0.2396 0.737

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alteration or replacement to allow full cycle MTSA operation. Improved methods will be vetted following integrated

subassembly testing.

Thermocouple measurements of the flow temperature at the test article inlet and outlet, as well as 5 equally

spaced external surface positions (TC_0 is nearest the inlet) are shown in Figure 7 for a representative adsorption

test. In this example, the test begins at when simulated ventilation gas is introduced and ends when the plotted CO2

concentration reaches 5000 PPM at 50 seconds.

This data clearly demonstrates the existence of an

adsorption front and associated release of

adsorption energy as the external temperature

nearest the inlet sharply rises at the beginning of

the test, whereas locations further downstream

react later, only as the upstream portions of the

bed begin to saturate. Note several departures in

this the data from ideal testing conditions. First

the starting temperatures should all be the same,

but a bias exists between the inlet temperature,

thermocouple positions 3 and 4, and the other

temperature measurements. This discrepancy may

be due to the ± 1 K accuracy of the type K

thermocouples used in the test. Furthermore, the

inlet temperature continually drops during the

test. This is an indication that the environment

temperature, to which the inlet tubing is exposed,

is not constant throughout the test. This variation as well as the overall temperature change during the test is small

and does not significantly impact the parameter that the test was designed to investigate, CO2 weight loading

percentage, and was expected from the control authority of the apparatus used to cool and maintain the external

environment temperature during the test. This is likely to impact the temperature data captured at each position in

forms not easily captured in a simple model.

Model temperature predictions for this test are given in Figure 8. Due to funding constraints and the difficulty

associated with accurately determining and modeling the dynamic test article environment, the model input and

output data were not adjusted since the effect of

the reduction in atmospheric temperatures extends

beyond the impact on inlet temperature. Still,

many similarities in the test and model data can be

seen which demonstrate model validity and the

data are provided for semi quantitate comparison.

Positions nearest the inlet have much greater

initial change than positions nearer the outlet.

Whereas the test data show peaks at location

temperatures not seen in the model data, the

difference between the inlet temperature and the

surface temperature are continuously increasing.

Furthermore, the magnitude of the average inlet to

surface temperature difference is similar for each

position. This difference is about 4 K in the model

and 5 K in the test after removing test data biases,

and demonstrates first order energy balance

agreement between the test data and model.

The performance of a model correlation based on the test article is probably not adequate to properly predict the

performance of the anticipated larger EDU. However, performance predictions are expected to be conservative.

The 7.5% equilibrium weight loading capacity empirically derived during model correlation was limited by C3,

resulting in only 6.0% adsorption at the time the test termination outlet concentration of 5000 PPM was reached. In

use, the MTSA must limit the outlet CO2 concentration to 21500 PPM. Thus the system will actually be able to

adsorb somewhat more CO2 than this model predicts. Further, for larger sorbent beds at a given flow rate, cycle

times will be increased and portions of the bed will be exposed to CO2 for longer duration, allowing those portions

to adsorb more CO2 and get closer to theoretical equilibrium (for the current temperature and pressure). In other

Figure 8. Temperature Response of Model Inlet, Outlet,

and Surface Positions.

Figure 7. Temperature Response of Test Inlet, Outlet, and

Surface Positions.

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words, the model prediction of a 7.5% equilibrium load is much less than the 19.5% that is predicted from

equilibrium states by the NaX vendor, UOP. This corroborates observations from previous tests that the amount of

CO2 that the bed can carry is not only a function of temperature and pressure but of time. One possible mechanism

for this phenomenon could be that the surfaces of the sorbent can saturate quickly, but it takes time for adsorbed

CO2 transfer from the surface deeper into the thickness of the sorbent material. Another explanation is that flow does

not pass through the bed evenly, due to partial or complete bridging of pore spaces that would take much longer to

reach equilibrium due to reduced local flow. These slower processes imply that the model control values derived

from these tests of a minute or less are less applicable at the longer time scales, ~15 minutes, which are expected in

the EDU and flight systems. Thus, additional model calibration from test data and possibly additional modeling

methods will be needed to handle simulation of larger systems.

The quality of the fit of model results against collected data demonstrate that the framework developed in

Thermal Desktop for simulating mass and heat transfer is adequate for the task of modeling the relevant transfer

mechanisms exhibited in the test article. The geometry of the EDU has additional implications on the local and

global performance and may not translate directly in modeling however. The local extraction efficiency term is

dependent on flow velocity and domain size. From a modeling and simulation time perspective, it is desirable to

change the discretization size for changes in geometry. Increasing the sorbent bed length without increasing the

number of discretizations, however, is expected to require an increase in the model’s local efficiency. This will be

the case in our transition from the small test article to the larger EDU as the EDU is approximately 2.25 times

longer. Predictive methods for performing this translation have been identified and will be evaluated in EDU test

model correlation. Since the sorbent article testing did not include data pertaining to the reaction of the system

during desorption, a generalized desorption methodology will require development and implementation in the EDU

model in order to capture the reconditioning of the bed during the desorption portion of the MTSA cycle.

B. Sublimation Heat Exchanger

The cooling mechanism that drives the capacity for adsorption in the MTSA design has gone through multiple

iterations. Originally a CO2 heat exchanger was designed to expand compressed liquid carbon dioxide, LCO2, as a

coolant to allow in situ resource utilization of the CO2 in the Martian atmosphere. To demonstrate the feasibility and

gather performance characteristics of such a system in MTSA application a Sublimation Energy Extraction Plate

(SEEP) test article was designed and tested.2 In investigating MTSA for lunar applications, water was considered as

a coolant due to the lack of a lunar CO2 resource and the fact that water is the current lunar baseline coolant and

would takes advantage of water’s greater potential for cooling capacity per kilogram. A modeling methodology for

sizing and simulating a water sublimation driven SHX was developed.4 Through implementation of the described

methodology it was found that very low vapor pressures at the desired minimum system temperature require large

heat transfer areas, which is not conducive to the development of a compact, lightweight cooling system. As it turns

out, the developed MTSA system may be applicable in the Lunar scenario without consumption of expendable

resources, as the system may be able to rely solely on a pressure (vacuum) swing and probably will not require a

temperature swing. (Unlike on Mars where the 0.8 kPa CO2 environment prohibits a pressure swing all together).

Thus, the EDU version of MTSA incorporates a LCO2-based SHX that will not be used on the moon, and the data

collected from the SEEP test article is an appropriate starting point for generation of a validated CO2 SHX model for

Martian use.

The thermodynamic cycle for the CO2 SHX is displayed in Figure 9. The initial state is represented by the blue

line near the top of the vapor dome Liquid CO2 is drawn from a storage tank at ~5500 kPa and undergoes Joule-

Thompson (isenthalpic) expansion into a tube where the reduced pressure results in flashing of the saturated liquid

to a liquid and vapor mixture. As the enthalpy is constant and energy is required to change the state of some of the

liquid to a vapor, this transformation results in a reduction of the bulk temperature of the flow. If the pressure at the

inlet of the SHX is sufficiently low as to reach the triple point (518 kPa and 216.6 K), some or all of this liquid will

solidify. Lower pressures still will allow all of the liquid to solidify and continue to drop in temperature. This part

of the process is seen between states A and B in Figure 9. In this example, the pressure at the SHX inlet is one

atmosphere, but lower pressures are desirable to reduce this temperature to increase heat transfer and efficiency at

low system temperatures. Extraction of energy from the warm MTSA (the MTSA starts out at ~280 K and through

extraction of energy is driven to ~210 K) forces sublimation of the solid CO2 at a relatively constant pressure and

temperature from states B to C. When all of the solid CO2 has sublimated, the gas warms toward that of the system

temperature in the process shown from point C to a position between C and D depending on the system temperature.

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Figure 9. Thermodynamic Cycle in SHX.

Three SEEP designs were tested and modeled. The data and model correlation for the SEEP design that was

found to be most applicable to the EDU and had the highest performance is given here to demonstrate the

applicability of the methodology developed to simulate free stream sublimation in SINDA/FLUINT. The SEEP

design is shown in Figure 10 consisting of 8 passes of one

0.097 inch inner diameter aluminum tube bonded to a 5 inch

long heated aluminum plate. This article was tested in a steady

state condition at a fixed flow rate of 4.9 kg/hr of CO2 at a

selection of temperatures ranging from 210 to 280 K.2

An analogous Thermal Desktop model of the SEEP is

shown in its entirety at the top of Figure 11, and in close up

detail in the lower portion of the figure. As in the SEEP, liquid

CO2 is drawn from a source at a given mass flow rate and sent

through a series of heated sections as well as unheated bend

lengths. Each of the heated lengths is connected to a boundary

node that represents the heater set point by a set of conductors

that represents the calculated thermal resistance form the heater

to the tube sections of 8.5 K/W. The fluid exhausts to a plenum

that represents the outlet pressure condition.

Modeling of gaseous and two phase flow in a pipe is a native capacity and common usage of SINDA/FLUINT.

In general however, the supplied fluid property files used to describe a condensable species do not extend below the

triple point into the solid state since it is uncommon to simulate a flowing solid. Modeling the phase change

enthalpy from solid to gas is critical in this application. The SINDA/FLUINT software, developed by Cullimore and

Ring Technologies, does have some tricks that were used to simulate entrained solid flow within a limited range

below the triple point pressure by altering the existing properties of the liquid state. In the provided property deck,

the phase change energy associated with the change from liquid to solid, 196.1 kJ/kg, was added over a 1 degree

temperature change from 216.6 K to 215.6 K. This enthalpy change is added over a finite band to prevent integration

CO2 tank conditions5.5 MPa, 292 K

Isenthalpic Expansion

to 0.101 MPa

Isothermal, sublimation

Isobaric,

warming

A

B

C

D

CO2 tank conditions5.5 MPa, 292 K

Isenthalpic Expansion

to 0.101 MPa

Isothermal, sublimation

Isobaric,

warming

A

B

C

D

Figure 10. SEEP Designs Relating to Small

Tube Single Configuration.

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errors across too small of a

temperature change. The density,

specific heat, and thermal

conductivity of CO2 at the triple

point were added as constants for

values below the triple point.

These single temperature values

are sufficient over the range of

temperatures used as they are each

weak functions of temperature.

On the other hand, the

saturation pressure is a strong

function of temperature, creating

significant limitations in the

application of this approximation.

The gradient in saturation pressure verses temperature is derived between the triple point and reference temperature

and applied to all values between. This linearization is applicable over small ranges below the triple point, but over

larger scales the true relationship is exponential.

The linearized approximation can result in violations

in the evaluation of the state of the solid/ vapor

mixture and results in runs being aborted. Through

experimentation with a range of reference

(minimum) temperatures, it was found that a

property file with a minimum use temperature of

175 K provided stable solutions whereas lower

values were too unstable for use in a model. This

175 K minimum temperature and the associated

minimum saturation pressure, 17.8 kPa, affect model

performance in two ways. Since the outlet of the

SXH is a full vacuum, vented CO2 will reach sonic

velocity resulting in choked flow. This outlet

condition defines the state of the fluid upstream.

With an outlet pressure of 17.8 kPa on the other

hand, low flow rates result in insufficient resistance

to keep the SHX pressure above this limit, resulting

in sub Mach outlet velocities. This condition

indicates that the model simulation contains some degree of error from an actual flow. This error manifests itself in

reduced simulation of heat transfer since the temperature throughout the SHX is higher than it would be in the actual

MTSA system.

The effect on the model can be seen in

comparison of the test results and model simulation

in Figure 12. The SEEP was operated at

temperatures of 210 K, 235 K, 260 K, and 280 K.

The model was run at these conditions as well as at

250 K and 210 K to better show the trend of the

model data. The model predictions from 280 K to

235 K are generally good for an effective system

thermal resistance of 7.0 W/K, with significant

divergence below 235 K.

Better understanding of the system

temperature range in which good model

performance transitions to significant under

prediction of heat transfer can be gained from

Figure 13. This plot gives several outlet conditions

including the Mach number, CO2 utilization

efficiency, fluid quality, and fluid temperature. The

Figure 13. Thermal Desktop Model of the SEEP in its Entirety (top) and a

Close-Up View (bottom) Showing Heated and Bend Lengths.

Figure 12. Extracted Heat Rate in Test and Model for

Selected Temperatures.

Figure 11. Outlet Conditions of the SHX Thermal Desktop

Submodel.

American Institute of Aeronautics and Astronautics

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SEEP model is expected to yield accurate results when the outlet model temperature and pressure are greater than

the minimum allowable fluid temperature (175 K) and pressure (17.5 kPa). Above this minimum, the model operates

with no violation in modeled physics. However, if during the simulation a temperature or pressure lower than these

limits is solved for in any location, the software resets these values to the minimum allowable, resulting in a

violation of the modeled physics. For example, for the 260 and 280 K set points, the outlet temperature (black line in

Figure 13) is well above 175 K and a good test to model correlation is seen in Figure 12. Note from the quality

reported at these temperatures (green line in Figure 13), that the input liquid has fully changed to a gas at the outlet

and that the Mach number (blue line in Figure 13), has reached unity as expected. At 250 K, the model outlet has

reached the minimum allowable temperature. At heater set point temperatures below 250 K, the model is limited to

the minimum pressure and temperature imposed on it by the limits of the fluid model. Actual system pressures and

temperatures would be lower than in the simulation. Simulations with boundary temperatures lower than 250 K can

be expected to contain some degree of heat transfer underestimation since the tube to wall temperature difference is

under predicted. Note however that at the 250 K and 235 K set points, the model outlet is constrained to the

minimum allowable fluid temperature, yet still shows good agreement with the SEEP data as shown in Figure 12.

Only at lower temperatures of 220 K and 210 K is the correlation poor. At these temperatures, the Mach number

drops below unity. This is a second departure from reality as the actual test article outlet pressure is much lower than

that allowable by the fluid model. In reality the flow would continue to expand and to attain Mach velocity at the

outlet, resulting in further reduction in system temperature. At operating temperatures below 235 K, system

temperatures and pressures are significantly affected and the available temperature delta is significantly reduced,

resulting in significantly reduced heat transfer.

In the end however the important detail in Figure 13 is the CO2 utilization efficiency, η, as defined by the

following equation where h refers to the fluid enthalpy and subscripts outlet, wall, and tank refer to the values at the

mixed mean outlet temperature, outlet wall temperature, and of the liquid CO2 in the storage tank (at 285 K):

tank

tank

hh

hh

wall

out

−

−=η (7)

In order for the SHX to make good use of the cooling potential of the CO2 coolant, the utilization efficiency

should be maximized. In Figure 13, utilization efficiencies are high for cases where the outlet quality is equal to

unity. This is because much of the available enthalpy change in the CO2 occurs in the phase change from solid to gas

as seen in the transition from points B to C in Figure 9. There in an important implication of high utilization

efficiencies on the accuracy of the model. Since the limitations of the fluids database reduce total heat transfer, and

thus utilization efficiency, the higher the utilization efficiency, the lower the possible error simulated heat transfer

The results of the SEEP test, particularly the

efficiency values, reveal the need for an improved

design. The path towards improved design can be

made clear by looking at why the SEEP design is

not efficient. Figure 14 shows the system

temperatures throughout the SEEP model. Each

line represents the average temperature of the

SEEP plate to which SHX tubing is attached. In

actuality, the SHX is one tube with several passes

along the plate (the plate simulating the sorbent

bed casing). In each case the fluid enters the tube

at a temperature of 216K. This indicates that the

fluid is at the triple point condition, where gas,

liquid, and solid CO2 coexist. As the flow travels

downstream, making additional passes across the

plate, pressure drop allows the remaining liquid to

boil resulting in a solid and gas only mixture.

Rather than the idealized and preferred path from

A to B shown in Figure 9, this process represents

movement to the right along the triple point line. Only when all of the liquid is removed from the flow can the

temperature drop to maintain the local equilibrium pressure while the solid CO2 sublimates. In the cases when the

SEEP plate is 280 K and 260 K, all of the CO2 sublimates and the temperature can alternately increase where it is

heated and decrease due to adiabatic expansion in the bends (for example, see location B7 in Figure 14). The

Figure 14. Modeled Temperature Response Throughout

the SHX for a Selection of Temperatures.

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problem with this SEEP design is twofold: the flow

rate and flow restriction are too high to allow all of

the CO2 to become a cold solid and gas mixture at

positions near the heat exchanger inlet. At lower

system temperatures this results in solid CO2

exiting the system before it can sublimate, leaving

it underutilized. This explains the very poor total

heat transfer in both the test and model. At a SEEP

plate temperature of 210 K the system temperature

is actually colder than the modeled fluid inlet

temperature.

Reducing either the resistance or flow rate

improves both characteristics. Figure 15 contains

the temperature profiles for a run with 30% of the

original flow rate. In this case, the transformation

from liquid to a solid entrained in gas occurs

completely at the inlet, allowing the inlet

temperatures to be significantly lower than with the

full flow rate. In this case the solid CO2 is fully

utilized at each temperature with cooler temperature

requiring more of the SHX length to do so, and rises

to just below the set point temperature indicating

high energy usage efficiency as well as little

potential for modeling error.

With an understanding of the relationship

between flow rate, flow resistance, and system

efficiency, the SEEP model was used to design a

MTSA EDU SHX. The optimal design for this

application is one that cools a reference mass

representing the mass of the EDU from 280 K to

210 K in the time required for one half of a cycle,

and does so with all of the solid CO2 being utilized

just short of the SHX outlet at 210 K. This results in

the optimized combination of the lightest system

mass achieved by minimizing tubing diameter for

the lowest CO2 mass usage.

Results for an optimized SHX are shown in Figure 16. Like the SEEP article this design presumes 8 passes but

the length of the EDU is twice that of the SEEP at 10

inches per pass. For this case, the presumed half

cycle time is 480 seconds and the target system

temperature of 210 K is reached in 460 seconds. As

in the example above, the inlet temperature is below

the triple point throughout the simulation and the

outlet temperature just reaches 175 K in the final time

step, indicating that the outlet has reached the

minimum saturation temperature allowed by the fluid

properties. Thus, the quality is below 1.0 and a small

amount of solid CO2 exits the system.

Note that since the flow rate in this design is

slower and the tube diameter is larger than the SEEP

test article, the Mach number is much lower than 1 as

shown in Figure 17. In application however, the

outlet Mach number will be equal to unity with

competing effects on the system. On one hand, the

Figure 15. Model Temperatures, 30% Nominal SEEP

Flow.

Figure 16. System Temperatures for Proposed EDU

SHX Design.

Figure 17. Outlet CO2 Utilization Efficiency (Compared

to 282 K) and Exit Mach Proposed EDU SXH Design.

American Institute of Aeronautics and Astronautics

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actual application will operate at lower SHX pressures. This will result in cooler inlet temperatures, raising the

potential for heat transfer in this region. With increased heat transfer, all of the solid CO2 would be used sooner and

little heat transfer would occur near the outlet. On the other hand, decreased pressure will decrease density which

reduces the local heat transfer coefficient, and increased velocity will decrease residence time which may prevent

CO2 for sublimating fully. While the uncertainty represents design risk, this design is believed sufficient for EDU

testing and will continue to be evaluated in follow on efforts.

C. Sorbent Bed

The CIHX is responsible for warming the bed to help drive off the CO2 captured by the sorbent bed when

pressure (a.k.a. vacuum swing) is insufficient alone. Utilization of the energy in the warm humid ventilation loop

gas is critical to the operation of a closed MTSA cycle on Mars. CIHX operation begins with the system temperature

near 210 K. As warm, humid gas passes through the CIHX, the contained water vapor condenses and freezes to the

walls, transferring energy from the flow to the CIHX in addition to the sensible heating of the walls from the non-

condensable gasses. The system heats until it reaches the melting temperature of ice at which point the ventilation

loop gas energy serves to melt the ice. The resulting liquid water must be wicked away and collected to prevent

revaporization into the ventilation gas which would slow warming. The system continues to warm to a temperature

high enough to ensure that all of the ice has melted in order to prevent accumulation in subsequent cycles that could

clog the system (~280 K). Since this process is limited by a finite flow rate and corresponding warming energy, and

adsorption cannot begin again until the upper temperature limit is met, the time required for the desorption half-

cycle is the key driver in determining system cycle time. Since longer cycle times require larger sorbent beds to

ensure that the two bed system can continuously remove CO2, and a larger bed requires more time to warm, a highly

efficient, low mass CIHX is critical to operability of the design.

In order to verify the operation

of a CIHX design under MTSA

flow conditions, test articles were

designed and manufactured as

shown in Figure 18 and tested.3 In

the figures, the large square cross

section represented the MTSA

design at the time. The CIHX is

represented by the channels on

top of the cross section, the

sorbent bed by the middle large

square, and the SHX by the lower

two flat channels. The CIHX

simulator to the right is intended

to simulate the surface area and

flow parameters of one of the CIHX channels in the circular tube. The thermal resistance to heat transfer from that

single tube is simulated with a thin fin section connected to a reference mass. This total simulator mass is indicative

of the amount of lumped mass cooled by one CIHX passage and the narrow fin represents the equivalent thermal

conductor from the CIHX to the center of the sorbent bed. Primary testing was carried out by cooling the system to

~210K and then passing a flow rate indicative of that in a single passage of a full CIHX. The flow consisted of N2

with a 286 K dew point mass fraction of water vapor at a temperature near 280 K. The modeling methods developed

for simulation of these test articles are applicable to each of the three test articles. However, only the data that is

most applicable to the configuration of the EDU, the 1/2” slow article, to the right in Figure 18, is shown here in

demonstration of model correlation and validation.

A view of the developed Thermal Desktop model applicable to each of these test articles is displayed in

Figure 19. This model contains the geometric representation of the test article itself, a fluid network to describe heat

transfer in the tube, and external conductors. The blue conductors represent very small conductance to a junction

that allows the volume average of all of the nodes to be determined for comparison against test article average

temperature measurements. A set of pink conductors connect the model exterior surfaces to a boundary node

representing the environment temperature.

Figure 18. Comparison of MTSA subassembly and Corresponding Test

Article Geometries for (a) ¼” Fast, (b) ½” fast (c) ½” Slow Configurations.

(Used in Model Correlation)

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The biggest challenge in modeling a CIHX in

Thermal Desktop is development and validation of a

methodology for simulating condensation of water

far below the freezing point of water. As discussed in

the SHX modeling section, SINDA/FLUINT does not

have the native capacity to model solids in fluid

models. In the case of CO2, a single set of sub-

freezing data could be used to yield an adequate

model despite the limit of a minimum allowable

model temperature. This method is not feasible with

water in the MTSA application. The

SINDA/FLUINT developer reports that they have

had success in modeling water with a minimum

temperature only as low as 258 K, 48 K higher than

the initial CIHX temperature of ~210 K. Since the

model cannot operate below the minimum allowable

fluid temperature, this limitation is not just one of

heat transfer; this would prevent the CIHX from

performing simulations below 258 K. A previously

documented methodology was proposed4 involving a

temperature transformation that would allow the

model to perform the simulation above this minimum

allowable model temperature and the results could be correlated to system temperatures as low as 210 K. In the end,

implementation was considered a significant challenge, requiring more time than was considered prudent for such a

model. Instead, the test article model makes use of an approach for modeling water where heat and mass transfer is

determined by assuming that water condenses evenly over the internal surfaces at a rate calculated from the

presumption that the outlet dew point temperature is in equilibrium with the outlet temperature.

This equilibrium outlet method differs from that used in

SINDA/FLUINT. A resistance network for mass transfer

modeling is shown in Figure 20. In this framework, mass

transfer coefficients developed from heat transfer analogies

would be applied to discretized areas along the tube surface

allowing for localized heat and condensation rates.

SINDA/FLUINT modeling routines also contain additional

resistance to mass transfer in the form of a condensation film

resistance6. To this, the resistance across the developed ice

layer can be added to capture the physics of the heat and

mass transfer in the CIHX. Not making use of the native

capacity for condensation modeling in SINDA/FLUINT

imposes limitations on the accuracy and degree of fidelity of

simulation. First, the opportunity to apply a film resistance is

removed, thus heat transfer, the basis for the mass transfer in

the equilibrium method, can be expected to be erroneously

high. Second, the total calculated mass transfer calculation is

based only on inlet and outlet conditions rather than at each

local discretization. Thus, the mass transfer rate and

associated heat rate via multiplication by the phase change

enthalpy of water is applied evenly in the generated simple

model.

Still much is accounted for in the developed model. As noted, the mass transfer first assesses the difference

between the inlet water content and the water content of the outlet presuming saturation at the outlet temperature.

The effect of this mass transfer is to impose a heat rate on the condensing surfaces which is distributed over the heat

transfer area. The latent heat of gas to water is applied where the system surface temperature is greater than 273 K

while the phase change enthalpy of liquid to ice is applied as well for temperatures below freezing. Sensible energy

exchange in the non-condensed water vapor is less than 3% of the total energy transferred from the flow and is

neglected. As the model surfaces warm to the melting point, energy must be expended to melt the ice that

Figure 20. Resistance Diagram Describing Heat

and Mass Transfer in the CIHX.

Figure 19. Description of Developed Thermal Desktop

CIHX Model.

American Institute of Aeronautics and Astronautics

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accumulates on surfaces. To do so, the sum of the energy required to convert condensed water into ice is tracked and

the model reduces the heat rate applied to the surfaces until the sum total of the ice energy is achieved. It is

presumed per the intent of the system design that liquid water is removed and that no revaporization into the flow

takes place. The latter can be presumed since the dew point of the flow entering the CIHX is always greater than the

temperature of the CIHX itself. This modeling method also allows for modeling of the resistance across the

developed ice layer; however this has not been implemented to date.

One additional limit is imposed on this methodology. The lower limit of the dew point is fixed to 270 K when the

outlet temperature is lower than this temperature. This mimics a trend seen in the test data showing that the outlet

humidity was limited to values just below the freezing temperature of water, 273 K. This modeling method allows a

decoupling of outlet temperature and dew point humidity as supported by model correlation.

Since the test article performance evaluation was

conducted in a warm environment at atmospheric

pressure, convective heat leak is a significant

component to the warming trend. To ensure this effect

was included, a passive heat up test was conducted on

the test article where it warmed from 210 K to 280 K

with no internal flow applied. To correlate, the

laboratory temperature (boundary condition in

Figure 20) and the convection coefficient (pink

conductors in Figure 19) were varied to see if a match

to the warming profile could be developed. An

excellent match between simulation and test warming

trends were attained with an environment temperature

of 292K and a convection coefficient of 4.1 W/K-m2

as shown in Figure 21. These values are reasonable

estimations for the temperature of the room and for a

mix of conduction through an insulating blanket and

free convection.

Early efforts at model correlation showed the simulated average article temperate profile was similar to that of

the test data, but the model warmed significantly faster. Several possible impacts were identified and alterations to

account for these impacts were evaluated, including entrance effects in the flow, and erroneous inlet or outlet dew

point measurements. In each case the impact was either seen to be negligible, cause poorer correlation, or cause

significant alteration on the resulting temperature profile. This type of model to test data disagreement suggests an

error in total energy balance; caused by either an inaccuracy in the total flow rate or the measured article mass. The

collected data are sufficient to directly assess the system energy balance by determining whether the total calculated

heat transfer from the flow matches that calculated by change in temperature of the reference test article mass. To do

so, flow data and the known average system temperature was used to determine four sources of heating. A passive

heat rate, q& passive, was determined by applying the model heat transfer coefficient, and environment temperature,

Tenv, as well as the average surface temperature of the article, Twall

( )wallenvcpassive TTAhq −= mod*& (8)

Where Amod is the external heat transfer area in the model. The sensible heat rate, q& sensible was determined for each

case via the energy balance:

)(** 2, inoutNpsensible TTCmq −= &&

(9)

In this equation, m& is the measured mass flow rate and Tin and Tout are the inlet and outlet temperatures. Similarly

the latent heat rate, q& latent is determined by:

)(** inoutfglatent AHAHhmq −∆= &&

(10)

Figure 21. Passive Test and Correlated Model Warm

Up Trends.

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Where the absolute humidity at the inlet and outlet conditions are described above in the article model description.

Finally, the passive heat rate was determined by applying Equation 8. The sum of the three inputs represents the

total heat rate applied to the system as a function of time. For comparison against these heat inputs and their sum

representing all of the heat inputs the system, the calculation of the heat rate absorbed by the test article, q& article, is

determined by:

t

TCmq

Alparticle

Article∆

∆=

** ,& (11)

In the equation marticle is the measured mass of the

test article prior to insertion into the test bed and

Cp, Al is the specific heat of Aluminum, the

material of construction for the entire article.

The results of these calculations over the

duration of the test are shown in Figure 22. One

thing this plot displays is the significance of the

latent heat as a source of heating as it is greater

than either passive or sensible heating. The other

thing to note is that the total calculated heat rate is

greater than the calculated net rate absorbed by

the test article throughout the test. The simplest

explanation for this difference is a thermal mass

contribution from the test system itself.

Additional sources of mass as well as sources of

conduction to mass include thermocouples, inlet

and outlet plumbing, and the material used to

insulate the article. Many of the sources of

additional mass, including plumbing and wiring,

are difficult to quantify due to significant thermal gradients making it difficult to directly measure these sources.

Presuming that the sensory data is valid, the total system energy can be compared with Equation 6:

( ) ( ) ( )( ) ( )initialfinalAlparticle

Tt

t

latentsensiblepassive TTCmdttqtqtq

final

−=++∫=

**

@

0

&&& (12)

From the test data a 1.33x multiplier is required on system mass to achieve balance. This multiplier was also

found to bring model temperature response in line with that of the collected test data providing some confidence that

the additional system mass is a likely explanation for the energy imbalance.

A comparison of test data to the final model data is given in Figure 23. Test inlet dew point and inlet temperature

were used to initialize the model as well as the initial system temperature. In general, the correlation between the

test article temperature response and the simulated article response is good. As expected due to the lack of a film

conductance in the resistance network and possibly ice resistance, the outlet ventilation gas temperature is closer to

the article temperature in the model than in the test. This contributes to the model article temperature rising faster

than that of the test. Comparison of the test outlet temperature and dew point temperature and their convergence just

below 270 K show the applicability to this limit in heat transfer calculations and yield favorable results despite a

much longer time until this convergence occurs in the model. Ice melting is indicated by the flattening of the article

temperature curve near 273 K.

While the tested and simulated article response is a close match, the time each takes to reach a reference

temperature of 283 K is 1245 seconds for the model vs. 1370 seconds for the test, a different of 9%. This is a similar

difference to those found in model variants that were generated for the other two articles shown in Figure 18. This

error is significant in the context of MTSA operation. Since the desorption half cycle can not end until it is assured

that all of the ice has been melted, the time it takes for the CIHX temperature to rise from 210 K to 283 K defines

the cycle time.

Figure 22. Test Flow Energy Contributions Compared to

Energy Available in Test Article Mass.

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It is difficult to say how alterations from the

CIHX test article (a circular tube) to the final

EDU design (containing high aspect ratio flow

channels) will affect the ability of the developed

model to predict performance. In general, it is

good that all of the parameters are on the same

order of magnitude, and that the hydraulic

diameter is nearly identical. In the end, the

Reynolds number will be a little over two times

the test value, a fairly close match. On the other

hand, an increased Nusselt number combined

with nearly 8 times the heat transfer area per

channel yields an expectation of significantly

larger heat transfer and presumably mass transfer.

In terms of the application of the model to the

EDU, this is thought to be beneficial. Increased

overall heat transfer indicates a greater

opportunity for the flow to come to equilibrium

with the walls of the test resulting in greater efficiency. As noted above, the model is best suited in high efficiency

applications where the fluid has the opportunity to come to equilibrium. This may have an impact on the 270 K dew

point assumption as the value may be lower in the EDU. Maintenance of the 270 K assumption does result in a

conservative assumption however, thus the model in its current form will be carried over into the EDU design.

Conclusions

A set of modeling methodologies, in part previously defined,4 have been updated and completed. These

methodologies were implemented in Thermal Desktop models and evaluated against sets of test data collected from

sorbent bed, SHX, and CIHX test articles. The sorbent bed and CIHX models were found to be valid over the range

of the test conditions and a good model correlation was achieved. Sorbent bed models indicate that the EDU sorbent

bed can be expected to capture more CO2 per mass of sorbent than in the test due to its larger size, larger allowable

outlet concentration, and increased cycle times. CIHX results indicate that the mass of items connected to the system

such as insulation, instrumentation, and pluming have a significant negative impact system performance and model

correlation, and that the developed model performs well when these additional masses are accounted for. SHX SEEP

test article results were shown to be valid in the case of high CO2 utilization efficiency. The verified model was used

to suggest an alternate design that attains high efficiency throughout the range of use temperatures, giving

confidence in the application of the model in future efforts. These models are now prepared for integration, update,

and evaluation in an EDU model. Details required for integrating the SHX and CIHX models together into the EDU

system model do not require alteration of the developed frameworks but each of the model components will require

additional development. The largest effort will be required in the sorbent model to capture the functional

dependencies pressure, temperature, and time on CO2 adsorption as well as the desorption process.

Future Work

A. An Integrated MTSA Subassembly EDU Model and Validation

Test and development of validated submodels prepares us for the end goal of a predictive integrated MTSA

subassembly EDU model that can be used in preparation for EDU testing and to serve as the basis for the

development of a validated full scale MTSA subassembly model. Construction of this model is already underway as

well as the manufacture of a PLSS-scale EDU. The EDU will then be tested in Paragon’s vacuum chamber in a

simulated lunar environment. The data will be used to validate the EDU model.

B. Recommendations for Model Improvement

There are several suggestions that should be considered to improve the generated submodels. Implementation

will depend upon the fidelity required in the model use as well as successful (or not) calibration to a fully integrated

MTSA subassembly EDU. These include:

Figure 23. Test Flow Energy Contributions Compared to

Energy Available in Test Article Mass.

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• Discretization of the CIHX mass transfer methodology, or implementation of potential improvements in

SINDA/FLUINT that can allow the native methodologies to be implemented. This will allow for more proper

distribution of condensation heat rates, and allow for localized ice collection tracking and melting routines.

• Address resistance across deposited ice in the CIHX. Methodologies for including this resistance have been

developed for cylindrical cross sections using Thermal Desktop pipes. This method would require alteration in

the current CIHX framework that does not use pipe entities. Applicability of the methodology would be

supported by the implementation of discretized mass transfer.

• Pressure drop modeling in the CIHX and sorbent bed. Currently, the pressure drop through the CIHX does not

include the effects of collected ice. Modeling of the expected change in pressure drop during the tests would aid

in the design and could be validated with EDU pressure data. In the SHX, pressure drop through the foam has

not been incorporated into the model. The functional dependence of pressure drop through the foam as

functions of the flow properties are known and can be modified for the impact of the NaX sorbent wash coat.

• Sorbent characterization. The Martian operational scenarios cannot be truly modeled without a characterization

of the performance of the foam across the parameters of temperature, CO2 pressure, and time. This

characterization can be used to support future design and EDU modeling.

• Improvement of SHX simulation. While the SHX model is expected to produce good overall heat transfer results

with the available properties, improvement of the property database will allow closer correlation and more

closely predict local temperatures in the SHX.

• Improvement in testing methods that allow for better collection of environmental data and development of model

inputs that allow for better direct comparison of test to model data. While this is not an improvement in the

model itself, it will result in better model correlation.

Acknowledgments

The authors gratefully acknowledge funding for this work through the NASA Small Business Innovation

Research (SBIR) program under Contract NNX08CC36P.

References 1Iacomini, C. S., Powers, A., and Paul, H. L., “PLSS Scale Demonstration of MTSA Temperature Swing Adsorption Bed

Concept for CO2 Removal/Rejection”, 2009-01-2388, 39th International Conference on Environmental Systems, Savannah, GA,

July 12 -July 16, 2009. 2Padilla, S., Iacomini, C., and Powers, A., “Investigating Liquid Carbon Dioxide as a Coolant for a MTSA Heat Exchanger

Design”, AIAA-2010-6014, 40th International Conference on Environmental Systems (ICES), Barcelona, Spain, July 2010. 3Padilla, S., Powers, A., Ball, T., Iacomini, C. S., and Paul, H. L., “Investigation of Condensing Ice Heat Exchangers for

MTSA Technology Development”, 2009-01-2387, 39th International Conference on Environmental Systems, Savannah, GA,

July 12 -July 16, 2009. 4Bower, C., Padilla, S., Iacomini, C. S., and Paul, H. L., “Modeling Of Metabolic Heat Regenerated Temperature Swing

Adsorption Subassembly For Prototype Design”, 2010-01-2387, 40th International Conference on Environmental Systems

(ICES), Barcelona, Spain, July 2010. 5Hwang, G.-J., Yeh, R.-H., and Chao, C.-H., “Measurement of interstitial convective heat transfer and frictional drag for flow

across metal foams,” Trans. ASME, February 2002, 124, 120-129. 6Cullimore, B. A., Ring, S. G., Johnson, D. A., “SINDA/FLUINT User’s Manual,” C&R Technologies, Littleton, Colorado,

Version 5.2, July 2009.

Acronyms

CIHX: Condensing Ice Heat Exchanger

CO2: Carbon Dioxide

EDU: Engineering Development Unit

FLUINT: Fluid Integrator

LCO2: Liquid Carbon Dioxide

MTSA: Metabolic heat regenerated Temperature Swing Adsorption

N2: Nitrogen

O2: Oxygen

PLSS: Portable Life Support System

ppi: pores per inch

PPM: Parts Per Million

SEEP: Sublimation Energy Extraction Plate

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SHX: Sublimation Heat Exchanger

SINDA: Systems Improved Numerical Difference Analyzer