Continuous System Modeling

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Object-oriented Modeling of Heat and Humidity
Budgets Of Biosphere 2 Using Bond Graphs
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What is Biosphere 2

• Biosphere 2 is an environmental research
  facility, located in the desert of Southern
  Arizona, that allows performing experiments in a
  materially closed ecological system under
  controlled experimental conditions.

• Biosphere 2 was built around 1990 with private
  funding and has functioned for almost 15 years
  already for various ecological experiments.

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Why Biosphere 2

• In Biosphere 1 (the Earth ecosystem), it is
  difficult to perform experiments, because of
  limited access to control variables.

• In Biosphere 1, it is easy to observe phenomena
  and report them, but it is difficult to interpret
  these observations in an objective fashion.

• In Biosphere 1, we are able to correlate data,
  but correlations per se do not establish cause
  and effect relationships.

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Biosphere 2 Construction

• Biosphere 2 was built as a frame construction
  from a mesh of metal bars.
• The metal bars are filled with glass panels that
  are well insulated.
• During its closed operation, Biosphere 2 was
  slightly over-pressurized to prevent outside air
  from entering the structure. The air loss per
  unit volume was about 10 of that of the space
  shuttle!

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Biosphere 2 Construction II

• The pyramidal structure hosts the jungle biome.
• The less tall structure to the left contains the
  pond, the marshes, the savannah, and at the
  lowest level, the desert.
• Though not visible on the photograph, there
  exists yet one more biome the agricultural biome.

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Biosphere 2 Construction III

• The two lungs are responsible for pressure
  equilibration within Biosphere 2.
• Each lung contains a heavy concrete ceiling that
  is flexibly suspended and insulated with a rubber
  membrane.
• If the temperature within Biosphere 2 rises, the
  inside pressure rises as well.

Consequently, the ceiling rises until the inside
and outside pressure values are again identical.
The weight of the ceiling is responsible for
providing a slight over-pressurization of
Biosphere 2.
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Biosphere 2 Biomes

• The (salt water) pond of Biosphere 2 hosts a
  fairly complex maritime ecosystem.
• Visible behind the pond are the marsh lands
  planted with mangroves. Artificial waves are
  being generated to keep the mangroves healthy.
• Above the cliffs to the right, there is the high
  savannah.

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Biosphere 2 Biomes II

• This is the savannah.
• Each biome uses its own soil composition
  sometimes imported, such as in the case of the
  rain forest.
• Biosphere 2 has 1800 sensors to monitor the
  behavior of the system. Measurement values are
  recorded on average once every 15 Minutes.

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Biosphere 2 Biomes III

• The agricultural biome can be subdivided into
  three separate units.
• The second lung is on the left in the background.

10
Living in Biosphere 2

• The Biosphere 2 library is located at the top
  level of a high tower with a spiral staircase.

The view from the library windows over the Sonora
desert is spectacular.
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The Rain Maker

• From the commando unit, it is possible to control
  the climate of each biome individually.
• For example, it is possible to program rain over
  the savannah to take place at 3 p.m. during 10
  minutes.

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Climate Control

• The climate control unit (located below ground)
  is highly impressive. Biosphere 2 is one of the
  most complex engineering systems ever built by
  mankind.

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Climate Control II

• Beside from the temperature, also the humidity
  needs to be controlled.
• To this end, the air must be constantly
  dehumidified.
• The extracted water flows to the lowest point of
  the structure, located in one of the two lungs,
  where the water is being collected in a small
  lake from there, it is pumped back up to where
  it is needed.

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The Conceptual Model
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The Bond-Graph Model
For evaporation, energy is needed. This energy
is taken from the thermal domain. In the
process, so-called latent heat is being
generated. In the process of condensation, the
latent heat is converted back to sensible
heat. The effects of evaporation and condensation
cannot be neglected in the modeling of Biosphere
2.
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The Dymola Model

• The overall Dymola model is shown to the left.
• At least, the picture shown is the top-level icon
  window of the model.

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The Dymola Model II
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The Dymola Model III
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Convection
Rth R T
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Radiation
Rth R / T 2
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Evaporation of the Pond
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Condensation in the Atmosphere
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Ambient Temperature

• The ambient temperature is computed here by
  interpolation from a huge temperature data file.

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Night Sky Temperature
25
Solar Input and Wind Velocity
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Absorption, Reflection, Transmission
Since the glass panels are pointing in all
directions, it
would be too hard to compute the physics of
absorption, reflection, and transmission
accurately, as we did in the last example.
Instead, we simply divide the incoming radiation
proportionally.
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Distribution of Absorbed Radiation
The absorbed radiation is railroaded to the
different recipients within the overall Biosphere
II structure.
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The Dymola Biosphere Package
We are now ready to compile and simulate the
Biosphere model.
(The compilation is still fairly slow, because
Dymola isnt geared yet to deal with such large
measurement data files.)
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Simulation Results I

• The program works with weather data that record
  temperature, radiation, humidity, wind velocity,
  and cloud cover for an entire year.
• Without climate control, the inside temperature
  follows essentially outside temperature patterns.
• There is some additional heat accumulation inside
  the structure because of reduced convection and
  higher humidity values.

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Simulation Results II

• Since water has a larger heat capacity than air,
  the daily variations in the pond temperature are
  smaller than in the air temperature.
• However, the overall (long-term) temperature
  patterns still follow those of the ambient
  temperature.

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Simulation Results III

• The humidity is much higher during the summer
  months, since the saturation pressure is higher
  at higher temperature.
• Consequently, there is less condensation (fog)
  during the summer months.
• Indeed, it can be frequently observed that during
  spring or fall evening hours, after sun set, fog
  starts to build over the high savannah, which
  then migrates to the rain forest, which
  eventually gets totally fogged in.

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Simulation Results IV

• Daily temperature variations in the summer
  months.
• The air temperature inside Biosphere 2 would vary
  by approximately 10oC over the duration of one
  day, if there were no climate control.

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Simulation Results V

• Temperature variations during the winter months.
  Also in the winter, daily temperature variations
  are approximately 10oC.

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Simulation Results VI

• The relative humidity is computed as the quotient
  of the true humidity and the humidity at
  saturation pressure.
• The atmosphere is almost always saturated. Only
  in the late morning hours, when the temperature
  rises rapidly, will the fog dissolve so that the
  sun may shine quickly.
• However, the relative humidity never decreases to
  a value below 94.
• Only the climate control (not included in this
  model) makes life inside Biosphere II possible.

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Simulation Results VII

• In a closed system, such as Biosphere 2,
  evaporation necessarily leads to an increase in
  humidity.
• However, the humid air has no mechanism to ever
  dry up again except by means of cooling.
  Consequently, the system operates almost entirely
  in the vicinity of 100 relative humidity.
• The climate control is accounting for this. The
  air extracted from the dome is first cooled down
  to let the water fall out, and only thereafter,
  it is reheated to the desired temperature value.
• However, the climate control was not simulated
  here.
• Modeling of the climate control of Biosphere 2 is
  still in the works.

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References I

• Brück, D., H. Elmqvist, H. Olsson, and S.E.
  Mattsson (2002), Dymola for Multi-Engineering
  Modeling and Simulation, Proc. 2nd International
  Modelica Conference, pp. 551-8.
• Cellier, F.E. (1991), Continuous System Modeling,
  Springer-Verlag, New York.
• Cellier, F.E. and J. Greifeneder (2003),
  Object-oriented Modeling of Convective Flows
  Using the Dymola Thermo-Bond-Graph Library,
  Proc. ICBGM03, 6th Intl. Conference on Bond
  Graph Modeling and Simulation, Orlando, Florida,
  pp. 198-204.

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References II

• Cellier, F.E. and R.T. McBride (2003),
  Object-oriented Modeling of Complex Physical
  Systems Using the Dymola bond-graph library,
  Proc. ICBGM03, Intl. Conference on Bond Graph
  Modeling and Simulation, Orlando, Florida,
  pp.157-162.
• Cellier, F.E. and A. Nebot (2005), The Modelica
  Bond Graph Library, Proc. 4th Modelica
  Conference, Hamburg, Germany, Vol. 1, pp. 57-65.
• Greifeneder, J. (2001), Modellierung
  thermodynamischer Phänomene mittels Bondgraphen,
  MS Thesis, Institut für Systemdynamik und
  Regelungstechnik, Universität Stuttgart, Germany.

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References III

• Greifeneder, J. and F.E. Cellier (2001),
  Modeling Convective Flows Using Bond Graphs,
  Proc. ICBGM01, 5th Intl. Conference on Bond
  Graph Modeling and Simulation, Phoenix, Arizona,
  pp. 276-284.
• Greifeneder, J. and F.E. Cellier (2001),
  Modeling Multi-phase Systems Using Bond Graphs,
  Proc. ICBGM01, 5th Intl. Conference on Bond
  Graph Modeling and Simulation, Phoenix, Arizona,
  pp. 285-291.
• Greifeneder, J. and F.E. Cellier (2001),
  Modeling Multi-element Systems Using Bond
  Graphs, Proc. ESS01, 13th European Simulation
  Symposium, Marseille, France, pp. 758-766.

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References IV

• Nebot, A., F.E. Cellier, and F. Mugica (1999),
  Simulation of Heat and Humidity Budgets of
  Biosphere 2 Without Air Conditioning, Ecological
  Engineering, 13, pp. 333-356.
• Cellier, F.E. (2005), The Dymola Bond Graph
  Library, Version 1.1.
• Cellier, F.E. (1997), Tucson Weather Data for
  Matlab.