This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Mathematical Modeling of Physical Systems
Thermal Modeling of Buildings II• This is the second lecture concerning itself with the thermal
modeling of buildings.• This second example deals with the thermodynamic budget
of Biosphere 2, a research project located 50 km north ofTucson.
• Since Biosphere 2 contains plant life, it is important, notonly to consider the temperature inside the Biosphere 2building but also its humidity
building, but also its humidity.• The entire enclosure is treated like a single room with a
single air temperature. The effects of air conditioning areneglected.
• The model considers the weather patterns at the location.
Mathematical Modeling of Physical Systems
Table of Contents• Biosphere 2: Original goals
Bi h 2 R i d l• Biosphere 2: Revised goals• Biosphere 2: Construction• Biosphere 2: Biomes• Conceptual model• Bond graph model• Conduction convection radiation
still-stand around 2003 due to lack of funding.• In 2007, management of Biosphere 2 was transferred to the
University of Arizona. Hopefully, the change inmanagement shall result in a revival of Biosphere 2 as anexciting experimental research facility for life sciences.
2
Mathematical Modeling of Physical Systems
Biosphere 2: Construction I• Biosphere 2 was built as
a frame constructionfrom a mesh of metalbars.
• The metal bars are filledwith glass panels thatare well insulated.
• During its closedoperation, Biosphere 2was slightly over-
Biosphere 2 rises, the insidepressure rises as well.
Consequently, the ceiling rises until the inside and outside pressure values areagain identical. The weight of the ceiling is responsible for providing a slightover-pressurization of Biosphere 2.
Mathematical Modeling of Physical Systems
Biosphere 2: Biomes I• The (salt water) pond
of Biosphere 2 hostsof Biosphere 2 hostsa fairly complexmaritime ecosystem.
• Visible behind thepond are the marshlands planted withmangroves. Artificialwaves are beinggenerated to keep the
• These elements have been modeled in the mannerpresented earlier. Since climate control was not simulated,the convection occurring is not a forced convection, andtherefore, it can essentially be treated like a conduction.
7
Mathematical Modeling of Physical Systems
Evaporation and Condensation• Both evaporation and condensation can be modeled either asBoth evaporation and condensation can be modeled either as
non-linear (modulated) resistors or as non-linear(modulated) transformers.
• Modeling them as transformers would seem a bit better,because they describe reversible phenomena. Yet in themodel presented here, they were modeled as resistors.
• These phenomena were expressed in terms of equations
• Hence the flow variable must be measured inkJ·kg_air/(h·kg_water).
9
Mathematical Modeling of Physical Systems
Evaporation and Condensation IV• The units of linear resistance follow from the resistance law:The units of linear resistance follow from the resistance law:
e = R·f. Thus, linear resistance is measured inh·kg_water2/(kJ·kg_air2).
• Similarly, the units of linear capacitance follow from thecapacitive law: f = C·der(e). Hence linear capacitance ismeasured in kJ·kg_air2/kg_water2.
Since the glass panels arepointing in all directions, itwould be too hard to compute the physics of absorption, reflection, andtransmission accurately, as we did in the last example. Instead, we simply dividethe incoming radiation proportionally.
evening hours that, after sun set,fog starts building up over thehigh savannah that then migratesto the rain forest, whicheventually gets totally fogged in.
Air humidity inside Biosphere 2 without air-conditioning January 1 – December 31, 1995
Mathematical Modeling of Physical Systems
Simulation Results IV• Daily temperature variationsy p
in the summer months.• The air temperature inside
Biosphere 2 would vary byapproximately 10oC over theduration of one day, if therewere no climate control.
• The humidity decreases as it gets colder.During day-time hours, it is higher than duringthe night.
13
Mathematical Modeling of Physical Systems
Simulation Results VI• The relative humidity is computed
as the quotient of the true humidityq yand the humidity at saturationpressure.
• The atmosphere is almost alwayssaturated. Only in the late morninghours, when the temperature risesrapidly, will the fog dissolve so thatthe sun may shine quickly.
• However, the relative humiditynever decreases to a value below
• Only the climate control (notincluded in this model) makes lifeinside Biosphere 2 bearable.
Relative humidity during three consecutive days in early winter.
Mathematical Modeling of Physical Systems
Simulation Results VII• In a closed system, such as Biosphere 2, evaporation
necessarily leads to an increase in humidity.y y• However, the humid air has no mechanism to ever dry up
again except by means of cooling. Consequently, thesystem operates almost entirely in the vicinity of 100%relative humidity.
• The climate control is accounting for this. The airextracted from the dome is first cooled down to let thewater fall out and only thereafter it is reheated to the
water fall out, and only thereafter, it is reheated to thedesired temperature value.
• However, the climate control was not simulated here.• Modeling of the climate control of Biosphere 2 is still
being worked on.
Mathematical Modeling of Physical Systems
References I• Luttman, F. (1990), A Dynamic Thermal Model of a Self-utt a , . ( 990), ynamic he mal odel of a Self
sustaining Closed Environment Life Support System, Ph.D.dissertation, Nuclear & Energy Engineering, University ofArizona.
• Nebot, A., F.E. Cellier, and F. Mugica (1999), “Simulationof heat and humidity budgets of Biosphere 2 without airconditioning,” Ecological Engineering, 13, pp. 333-356.
• Cellier, F.E., A. Nebot, and J. Greifeneder (2006), “BondGraph Modeling of Heat and Humidity Budgets ofBiosphere 2 ,” Environmental Modeling & Software,21(11), pp. 1598-1606.
Mathematical Modeling of Physical Systems
References II
• Cellier F E (2007) The Dymola Bond Graph• Cellier, F.E. (2007), The Dymola Bond-Graph Library, Version 2.3.
• Cellier, F.E. (1997), Tucson Weather Data File for Matlab.