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SimAUD 2018 June 05-07 Delft, the Netherlands
© 2018 Society for Modeling & Simulation International (SCS)
Coupled Modeling and Monitoring of Phase Change
Phenomena in Architectural Practice
Billie Faircloth1, Ryan Welch1, Yuliya Sinke2, Martin Tamke2, Paul Nicholas2, Phil Ayres2, Erica
Eherenbard1, Mette Ramsgaard Thomsen2
1 KieranTimberlake
Philadelphia, USA
bfaircloth@kierantimberlake.com
2 CITA Centre for IT and Architecture
Copenhagen, Denmark
martin.tamke@kadk.dk
ABSTRACT
Geometries designed with carefully controlled heat
absorption and heat transfer profiles often elude designers
because of the complexity of thermodynamic phenomena
and their associated discipline-specific numerical models.
This project examines the behavior and design of geometries
associated with non-isolated thermodynamic systems by
constructing a material prototype that is fully coupled to a
mechanistic modeling interface. The prototype, a facade
system of phase change materials, was mounted on an
adjustable outdoor testbed. Its baseline geometry was
continuously monitored over two seasons and characterized
with respect to variation in liquid and solid states. The
mechanistic model, which uses a finite element method,
incorporates multiple components including geometry,
orientation, material properties, context geometry (e.g.
buildings and vegetation), weather, climate, and an array of
sensors monitoring the real-time temperature distribution of
the testbed and phase-change materials. Data were
continuously collected from the testbed and used to calibrate,
validate, and verify the mechanistic model. In turn, the
calibrated mechanistic model provided a platform for the
design of new facade geometries and predictions of their
behavior. The project demonstrates an integrative modeling
approach, orchestrating handshakes and feedback loops
between disparate spatial and temporal domains, with the
ambition of defining a cogent design framework for practices
that are trans-scalar, trans-temporal, and trans-disciplinary.
Author Keywords
Thermodynamics; System boundaries; Phase change
materials; Mechanistic model.
ACM Classification Keywords
D.1.7 Visual Programming; D.2.2 Design Tools and
Techniques; I.6.4 Model Validation and Analysis.
1 INTRODUCTION
The architectural design community has difficulty
integrating methods to manipulate, measure, and model
transient phenomena associated with open thermodynamic
systems. Phase transition, such as the melting from solid to
liquid, is one of these observable phenomena. It is influenced
by the nuanced interaction between geometry, context,
material properties, weather, and the mechanisms of heat
transfer. Whereas the assumption of steady-state conditions
provides a well-defined system boundary to study heat
transfer; and, whereas numerical and analytical approaches,
such as finite element analysis (FEA), discretize heat flow at
an unlimited number of points across a given domain in order
to identify boundary conditions; these methods are
associated with multiple scales and disciplinary-specific
workflows [1]. They are limited in their capacity to handle
dynamic information flows, presume an analytic, rather than
generative, design approach, and are indicative of a complex,
multi-scalar, and multi-method modeling and simulation
challenge within the design community [8].
Actual material behavior is an entanglement of macro and
micro interactions and extensive and intensive properties
across spatial and temporal domains [12]. For instance,
architectural material assemblies continuously accumulate
and dissipate heat which engender small, large, symmetrical,
and asymmetrical thermal gradients. Thermal gradients,
which are likewise a transient phenomenon, are attributable
to the interaction between environment, material properties,
local surface features, surface geometry, and overall form.
There is, thus, the potential to investigate a multi-scalar,
multi-method design and modeling approach for
architectural assemblies using methods from the fields of
architectural design, thermodynamics, and materials
engineering in which (1) using full-scale prototypes, the
actual thermal behavior of a material system is continuously
measured and characterized; (2) using a mechanistic model
of coupled components and real-time measurement, the
thermal behavior of the same system is simulated, calibrated,
and validated; and (3) using a calibrated and validated
simulation platform, designers can author and predict
nuanced heat transfer profiles for new surface geometries,
and thereby fabricate, measure, and characterize their
performance.
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Here we present results from a six-month study that
implements this modeling approach using organic, paraffin
wax phase change materials (PCMs). PCMs undergo a phase
transition from solid to liquid, and conversely liquid to solid,
at a designated temperature. In doing so, PCMs are capable
of maintaining that temperature while absorbing or releasing
large quantities of energy. In architecture, PCM-based
thermal energy storage systems seek to reduce overall
building energy use, reduce peak energy loads, minimize
HVAC system sizing, and improve overall thermal comfort
[2, 4, 10]. Experimentation with PCM-integrated elements,
including walls, floors and ceilings, are systematically
reviewed in the literature [3, 6, 13]. PCM applications
include microencapsulants (10 - 1000 µm spheres) mixed
with materials such as gypsum to create wallboard, or cement
to create mortar [7, 9]. They also include macroencapsulants
(≅ 4cm x 4cm x 1cm bars) integrated into climate
management layers such as the commercially available
BioPCM®. PCM glazing experiments include encapsulation
between several glass or plastic layers and incorporation into
slats, louvers, and shading fins [11].
Ours is a non-normative application of PCMs: they are bulk-
cast into formed panels and exposed to direct solar radiation
and extreme differences in temperature. While absorption
and release of energy is the primary interest of PCM wall
applications, our interest in PCMs stems from their capacity
to act as a visual register of thermodynamic behavior and,
correspondingly, as a tool for qualitative validation of
predictive modeling methods. Used thus, they offer the
possibility to connect behavior at the material scale to a
nested series of larger length and time scales; and the
opportunity to calibrate, via design, these larger scales to
steer phase transitions within the PCM for the purpose of
achieving particular desired visual effects and expressions.
2 METHODS
In order to study the relationship between model geometry
and PCM melting behavior, an adjustable apparatus
consisting of 23 rhombic panels was fabricated, assembled,
and monitored on-site in Copenhagen, DK for a period of six
months. An accompanying digital mechanistic model was
developed to form predictions of melting behavior based on
empirical data for internal calibration.
2.1 Panel Geometry
Variations in panel geometry were explored to test the
hypothesis that local differences in the quantity of PCM (in
terms of surface area to volume ratio) and exposure to solar
radiation should yield measurable differences in the local
rate of melting. Five panel designs were developed as mesh
geometries in Rhinoceros3D using the Grasshopper visual
scripting environment. A baseline geometry was established
based on a bi-directional sinusoidal pattern applied to the
outside surface, with a total depth of 40mm. Two variations
employed horizontal and vertical displacements,
respectively, to the baseline pattern in order to study the
effect of varied solar exposure on melting behavior, under
the constraint of constant PCM volume. A third variation
reduced the amplitude of the sinusoidal pattern by 50%, and
a fourth variation reduced the overall scale of the sinusoidal
pattern in all dimensions by 50%.
These last two variations permit study of how volume and
surface area influence melting behavior; each has half the
overall PCM volume of the baseline, while the latter has
significantly greater exposed surface area than the former.
Figure 1. Panel geometries: (top row, l-r) baseline, horizontal shift,
vertical shift, (bottom row, l-r) shallow, dense.
2.2 Panel Fabrication
To encapsulate the fluid volume of each PCM panel, a
vacuum-formed thermoplastic shell was constructed. Panels
were assembled from two layers of 1mm thick Vivak®
polyethylene terephthalate glycol-modified (PETG) sheet.
PETG was selected based on its ability to take on complex
geometries when thermoformed and for its visual
transparency, which permits direct visual observation and
video recording of melting behavior. The outer layer of each
shell was thermoformed onto a medium density fiberboard
(MDF) surface, milled to form the positive of the digitally-
modeled PCM pattern. After thermoforming, the outer layer
of PETG was heat-press bonded along its perimeter onto a
flat, inner PETG surface, and additional mechanical through-
fasteners were added periodically at sinusoidal valleys to
prevent buckling under static PCM pressure.
Two types of PCM, Rubitherm® RT 6 and RT 10, were
selected for study based on nominal melting points of 6°C
and 10°C falling slightly above typical dry bulb temperatures
experienced in Copenhagen during the initial study period.
Hence, the combination of daytime solar radiation and
nighttime conductive heat loss would offer a high likelihood
of complete cycling between solid and liquid state over a
typical 24-hour period. The two PCM types were distributed
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among the 23 panels such that every unique combination of
panel geometry and material occurred at least twice.
Figure 2. Panel fabrication and assembly.
Figure 3. Panel distribution on testbed. Horizontal and vertical
hatches indicate panels containing RT 6 and RT 10 PCM,
respectively. Red indicates panels equipped with sensors.
Figure 4. Detail of sensors, conductive tape, and interface port.
One panel of each unique type was furnished with an array
of Maxim DS2438 1-Wire™ temperature sensors (±0.5°C
accuracy) to monitor the state of the PCM over the duration
of the experiment. Sensors were conformally coated to
protect from moisture, affixed to the interior of the panel with
epoxy cement, and wired with conductive tape to an interface
port at the edge of each panel for connection to a Wi-Fi
enabled node.
Figure 5. Adjustable testbed and monitoring equipment on-site
2.3 Testbed and Instrumentation
Encapsulated PCM panels were mounted to the front face of
the adjustable testbed enclosure and placed in an exterior
courtyard where they remained for the duration of the
experiment. The testbed measured approximately 1.2m x 2m
x 2.5m and consisted of a plywood frame with infill
expanded polystyrene (EPS) foam insulation. The frame was
affixed to a plywood and polyisocyanurate (PIR) foam base
that was anchored to earth screws and sat slightly above the
ground. The base incorporated a horizontal hinge along its
front face to permit changing the vertical orientation of the
PCM panels. This allowed incident solar radiation to be
maximized in response to changing solar altitude across
seasons. The narrow ends of the testbed were sealed with
Thinsulate™ fabric to permit maintenance access to the
otherwise fully enclosed interior. As the interior was
unconditioned and normally unoccupied, it operated in a
passive, free-run condition based on climatic forces.
A second set of 19 1-Wire temperature sensors was arrayed
across the inside face of the PCM panels and throughout the
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testbed interior to monitor the interior environment of the
apparatus and its contribution to PCM melting behavior.
The array of temperature sensors was connected to a Wi-Fi-
enabled node running Pointelist®, an ecosystem for wireless
collection of high-density sensor data. The node logged
readings from each sensor in five-minute intervals and sent
data to the Pointelist web API for subsequent viewing and
analysis.
Ambient conditions at the testbed site were monitored by a
local weather station (Ambient Weather® WS-1400-IP) and
reported to the Personal Weather Station service of Weather
Underground. This device was mounted adjacent to the
testbed at a 4m elevation and gathered various relevant
quantities, including dry bulb temperature, humidity, wind
speed and direction, and total horizontal radiation.
A time-lapse camera (WansView®) was mounted in front of
the testbed to monitor changes in PCM state, direct sunlight,
and cloud cover in five-minute intervals to coincide with
temperature recordings.
2.4 Mechanistic Model
A mechanistic model was developed to predict the behavior
of PCM under varying environmental conditions and
calibrate predictions against observed behavior. The model
comprises a series of custom Grasshopper components that
cover the following modules: climate, context, sensor,
material, geometry, simulation, and results.
The climate module describes the ambient environmental
conditions surrounding the physical testbed in terms of dry
bulb temperature, wind speed, diffuse horizontal radiation,
direct normal radiation, and solar angle. These are sourced
variously from typical meteorological data, airport data, and
local weather station data, depending on the time-frame of
the simulation and the availability of data from each source.
The context module represents the geometry of neighboring
structures and vegetation that would potentially shade the
physical model from direct or diffuse radiation. It accounts
for both permanent structures and vegetation with a variable
shading coefficient.
The sensor module connects the mechanistic model to the
array of temperature sensors describing the interior
conditions of the testbed as well as to the sensors embedded
within the PCM medium. The former serves to define the
interior boundary condition of the simulation while the latter
serve as calibration points against which the predicted
behavior can be validated.
The material module describes the thermodynamic
properties of PCM for use in the run-time simulation. These
include the heat of fusion, melting point range, and liquid-
and solid-state properties of density, heat capacity, thermal
conductivity, and albedo.
The geometry module translates the bounding surfaces of the
encapsulated PCM form into a 3D polyhedral finite element
mesh, whose resolution may be defined through an input
parameter. The module pre-computes the direct and diffuse
shading coefficients for each mesh face of the exterior
boundary, which frees the run-time simulation from the
burden of occlusion calculations. Neighbor-neighbor
relations are automatically generated so that at any point
during the simulation, the heat flow between neighboring
elements may be computed based on the local temperature
gradient and the area of their common face and cached at
each time step. Due to the nonlinear diffusion behavior in the
phase-change regime the complete set of heat flows are
calculated at each time-step and subsequently applied to each
element, which—depending on the element’s current
phase—may have the effect of changing its temperature,
phase, or both. Hence storing the heat flows independently
permits parallelization of the run-time computation.
Figure 6. Grasshopper components of mechanistic model
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Figure 7. Exploded isometric view of instantaneous heat flow
between neighboring finite elements.
The simulation module allows the user to select a date, time
range, and finite element mesh to predict behavior of a panel
or to calibrate its phase change behavior against sensor data
collected over the selected time period. During the
simulation, a splash screen displays metrics describing
boundary conditions (interior and exterior temperature, wind
speed and direction, direct and diffuse solar radiation, and
data source); features of the finite element model (minimum,
average, and maximum values for temperature and phase);
and calibration metrics (variance between measured and
predicted values at each calibration sensor location).
Figure 8. Simulation splash screen with calibration metrics.
2.5 Interaction Between Testbed and Model
The mechanistic model serves a dual purpose: it offers a
platform for design iteration and material selection; and it
provides a means of validating its predictions using empirical
data gathered from sensors embedded in the PCM medium.
Prior to engaging in physical prototyping, one may begin
with a set of preliminary simulation settings (e.g. spatial and
temporal resolution, time frame, etc.) and simulate the
expected behavior of a given PCM, geometry, and siting.
Based on initial predictions one may choose to modify
material properties, such as selecting a PCM with a higher
melting point or greater heat of fusion. Alternatively, one
may choose to modify geometry or siting to enhance the
frequency and variety of predicted melting behavior in
response to design goals. Likewise, one may compare the
relative effects of systematically changing geometric
properties (depth, surface area, or orientation) in order to
guide the refinement and selection of panel types for
subsequent fabrication.
Figure 9. Digital design iteration and material selection workflow.
Following a phase of prototyping and data collection, the
time-series temperature values predicted by the mechanistic
model are compared to the corresponding empirical
temperature data collected by the calibration sensors
embedded in the PCM medium. Standard deviations between
predicted and observed behavior are calculated automatically
within the simulation component, provided calibration
sensor data is available for the chosen time period. Hence,
numerical refinements to the material properties and
simulation settings may be automated through optimization
tools such as Grasshopper’s Galapagos GA solver. Where
numerical refinements fail to resolve differences between
predicted and observed behavior, time-series graphical
comparisons and video footage are employed to discover
systematic deviations due to real-world phenomena not
adequately represented in the model (see further discussion
of buoyant effects).
Findings from this calibration exercise establish the range
over which the mechanistic model yields accurate
predictions and thus permits further design iteration and
material selection. Thus, one can alternate between these two
modes of operation with each series of prototypes.
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Figure 10. Calibration workflow for refining simulation settings and
material properties.
3 FINDINGS AND DISCUSSION
Two sets of experiments conducted between March and
September of 2017 attempted to prove the viability of the
design and calibration workflow described above.
3.1 Initial Experiment
The initial experiment using the five aforementioned panel
types was conducted from March 15th to April 18th, 2017 and
attempted to validate three hypotheses: different PCMs
should exhibit similar patterns of melting in panels of the
same geometry, but at distinct temperatures and times;
variations in panel surface geometry should exhibit local
variations in melting rate; and the mechanistic model should
correctly predict these trends.
Time series temperature data and video recordings
confirmed that panels containing RT 6 PCM exhibited
melting behavior before their counterpart panels containing
RT 10, which has a higher melting point temperature. While
the precise duration of these phase transitions differed
slightly between predictions and observations, the
mechanistic model correctly predicted the start time of
melting in both cases as well as the relative difference in
complete melting between the two materials.
At the local scale of the surface texture, it was observed that
the melting occurs first at the shallowest areas of the panel.
This behavior is expected because these regions have the
highest surface area to volume ratio, and hence the least heat
capacity per unit of conductive and radiative heat gain. This
observation was also correctly predicted by the mechanistic
model.
Figure 11. Local melting behavior in response to changes in depth.
By extension, the shallow panel types (4 and 5), which
contain less PCM per unit of surface area, completed melting
significantly earlier than the other three panel types.
Embedded sensors inside the PCM also confirmed that the
shallower panels exhibited a higher rate of temperature
change than their deeper counterparts during these phase
transitions.
Figure 12. Differential behavior of adjacent panels with different
PCM depth.
Comparison of the deeper panel types, which differ in the
displacement rather than depth of sinusoidal pattern, yields
less pronounced differences than in comparison to shallower
panels. Since these three panel types have approximately
equivalent surface area and volume, their principle
difference lies in the orientation of particular surfaces toward
or away from direct sunlight. Hence, the differences ought to
be perceived only at a highly localized scale, not
comprehensively for an entire panel. Indeed, footage reveals
that the panel with a vertical shift, which has roughly half of
its peaks oriented with a broad surface toward midday sun,
begins melting somewhat earlier than the other two panel
types.
One important feature of the observed behavior that was not
captured in the mechanistic model was the buoyant
convection of the liquid PCM during the later stages of the
melting regime. The PCMs under investigation exhibit
significant thermal expansion when they transition from
solid to liquid. At the onset of melting, this is not problematic
because the liquid is confined to small regions and the
surface texture remains the dominant factor driving melting
behavior. However, as more of the material transitions into
the liquid state, the buoyant effects begin to dominate as the
lower density liquid finds a continuous path for rising to the
top where it accelerates the melting of any residual solid
PCM. At this point, any trace of effects due to panel
geometry is confined to the bottom of the panel where solid
material remains.
While in principle, the finite element method employed in
the mechanistic model could be extended to consider
buoyant convection, the visual effects of this buoyancy were
considered undesirable, and in subsequent design iterations
(discussed further), effort was made to compartmentalize the
PCM medium and limit the degree to which liquid-state
PCM could rise to the top.
In contrast to melting behavior, the process of solidification
was much more gradual and uniformly distributed
throughout the PCM medium, suggesting little dependence
on surface geometry. The solidification regime was
characterized by local crystal formation throughout the
PCM, suggesting that the liquid medium was at internal
equilibrium prior to changing phase. This can be understood
87
based on two observations: the liquid state permits more
rapid heat diffusion via convective flow; and the nighttime
ambient temperatures tend to fall gradually compared with
the rapid daytime temperature rise brought on by solar
radiation. Furthermore, it is likely that microscopic effects
below the resolution of the FEM contribute to the observed
hysteresis, as observed by others [8]. Due to this feature, and
the fact that solidification typically occurred at night when
no one was present to observe it, further analyses and design
iterations focused exclusively on melting behavior.
3.2 Model Verification and Calibration
Model verification was performed in the results module of
the mechanistic model. Following each simulation, a graph
of predicted and observed behavior was generated to identify
systematic variations at each calibration sensor location. In
the solid phase and during the initial melting, these graphs
typically showed agreement between predicted and
measured values within the reported accuracy of the sensor.
However, wider discrepancies arose toward the end of the
melting regime and persisted throughout the liquid phase.
The initial deviation is likely due to the aforementioned
effects of buoyancy, which were observed in the physical
testbed but not represented in the mechanistic model.
Subsequent deviations in the liquid phase tended to show that
measured values were significantly higher than predicted.
One possible explanation for this observation is the sensors
may be exposed to direct solar radiation in the liquid phase
due to the transparency of the PCM. Hence, measured values
may not accurately reflect the local temperature of the
medium.
Figure 13. Validation of melting behavior for panel type 4.
3.3 Model Conversion
Following calibration of the mechanistic model and
determination of appropriate simulation parameters and
range of predictive capacity, a second round of design
iteration was conducted. In order to maximize the frequency
and duration of the melting phase and to account for the
warmer season of this experiment, Rubitherm RT 18 HC was
selected as the PCM for all 23 panels. This material has a
nominal melting point of 18°C and a higher heat of fusion
(260 kJ/kg) compared to both RT 6 and RT 10 (160 kJ/kg).
This study began with a routine for linearly varying PCM
depth as a height-field based on distance from a set of control
points, resulting in a form resembling a voronoi diagram.
The mechanistic model predicted that melting would begin
at each control point and expand radially. Indeed, this
behavior was observed at the onset of melting. However, the
continuity of the PCM material in this panel geometry
exacerbated the buoyant effects observed previously.
Figure 14. Voronoi panel with sequential predictions of radial
melting behavior
Figure 15. Array of panels types whose melting behavior intends to
reveal lines, dashes, deep dashes, and dots.
A subsequent exercise attempted to explicitly resolve the
top-down melting of the voronoi experiment by
compartmentalizing the fluid volume and limiting buoyant
flow. It also sought to demonstrate more refined design
control of material behavior by introducing a set of panels
whose variation was not apparent in the exterior form, but
revealed itself through the melting process. Therefore, the
inner surface of PETG was thermoformed to establish
varying material depth while the exterior surface was molded
to a uniform cross-hatch. Under this modification, the testbed
appears undifferentiated in the solid phase, while the melting
reveals transient directional patterns of dashes and dots
according to varying depth of the inner surface. Four panel
types incorporating variations on lines, dashes, and dots were
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distributed across the testbed and monitored from June
through September of 2017.
The results of this concluding exercise were largely
successful. Melting occurred first in the intermittent regions
of minimal material depth, leaving behind discontinuous
patterns of solid material. Thus, for the brief period of
melting, the selected patterns were observable at the scale of
the entire 23-panel facade.
Figure 16. Variations in panel behavior in situ as compared to
simulation.
4 CONCLUSION
A multi-scalar, multi-method design and modeling approach
couples the behavior of full-scale material prototypes to a
mechanistic modeling framework through continuous cycles
of measurement and calibration. This approach recognizes
that material behavior cannot be accurately captured,
controlled, or manipulated through a single disciplinary
method and that physical prototyping and simulation can
work together to integrate multiple methods. This research is
motivated by the aim to provide designers with the means
and methods to work directly with complex transient
phenomena, such as heat transfer, which normally lie beyond
their purview. Individuals with backgrounds in architectural
detailing, architectural computation, computer science,
chemical physics, materials engineering, and sculpture
jointly engaged processes to author surface geometry and
predict PCM melting behavior.
A mechanistic model can be internally calibrated and remain
only partially validated due to its inability to account for all
transient behavior. Comprehensive modeling of PCMs
remains a formidable challenge [5]. A highly localized
process of phase change is driven by heat transfer
mechanisms that occur at multiple scales. On account of the
complexity of these phenomena and the non-standard and
dynamic conditions of our application, our mechanistic
model did not attempt to address buoyancy effects or sub-
millimeter scale heat transfer. This points to conditions that
must be placed on mechanistic model specifications, and to
the value of continuous observation in building tacit
knowledge of material behavior. Control of transient
behavior was achieved to a degree, indicating opportunities
elsewhere for designers to engage in complex modeling and
feedback through the coupling of models and prototypes.
ACKNOWLEDGMENTS
We wish to thank Patrick Weiss, Suzanne Mahoney, Eric
Eisele, Christopher Connock, Angelos Chronis, and Asya
Ilgun for their contributions to modeling and prototyping.
We are grateful to KieranTimberlake and CITA for their
vision and support, and to the Velux Foundation, which
provided funding for this research through the Velux Visiting
Professor Programme.
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