Presenting an Accessible yet Rigorous  Development of the Zone Temperature Equation: An Important Thermodynamic Result Inherently Interesting and Educational

Sheldon Jeter; christopher fernandez

Download Paper | Permalink

Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: Energy Conversion and Conservation Technical Session 5: Strategies for Increasing Classroom Engagement
Page Count: 19
DOI: 10.18260/1-2--41306
Permanent URL: https://peer.asee.org/41306
Download Count: 238

Request a correction

Paper Authors

biography

Sheldon Jeter Georgia Institute of Technology

visit author page

Sheldon M. Jeter has mechanical engineering degrees from Clemson, the University of Florida, and Georgia Tech. He has been on the academic faculty at Georgia Tech since 1979 and will retire in August 2022. He has written over 250 refereed journal articles and conference papers and numerous research reports and other articles. He has supervised 16 Ph. D. graduates and numerous other research students. His research interests are thermodynamics, experimental engineering, heat and mass transfer, solar energy, and energy systems including concentrating solar power and other solar issues, building energy systems, and HVAC issues in health care facilities.

visit author page

author page

christopher fernandez

Download Paper | Permalink

Abstract

The Zone Temperature Equation (ZTE) is a time-derivative equation of for the temperature of a building “zone”, which is a control volume representing a part or the whole of the conditioned space in a building conditioned for thermal environmental control. As such the ZTE is an important tool used in building energy systems simulations. The usual version of the equation is probably best stated in the references for EnergyPlus the widely used and generally well-regarded building energy simulation package. This program was developed as a major project supported by the US Department of Energy involving various national labs and contractors and with substantial participation by private industry. The resulting program is, with good reason, widely used around the world. Indeed, EnergyPlus appears to be the first popular building energy simulation program that is intended to be thermodynamically rigorous, in that many previous simulation programs were primarily hourly load calculations. Indeed, the ZTE, which represents combined energy and mass conservation, is presented along with conservation equations for moisture and carbon dioxide concentration in EnergyPlus. The ZTE in EnergyPlus can be shown to be accurate for its intended use; nevertheless, it has some theoretical deficiencies, one of which could have practical implications. Obviously, this equation is important for its role in such an important simulation and is interesting pedagogically in itself as being a rather ingenious combination of the mass and energy conservation principles. Junior or senior students in mechanical or related engineering interested in building energy systems or related thermal systems should be aware of this equation, especially the rigorous and thermodynamically exact form presented in the present paper. Such students should have finished the usual first semester thermodynamics course and be well aware of energy and mass conservation as well as the properties of ideal gases. These are the only preparation needed to fully understand and appreciate and even apply the ZTE. For classroom presentation at this level, at least two approaches are feasible (1) the equation can be presented by quotation from the relevant reference material with some heuristic justification or (2) if time permits the equation can be developed from first principles and then interpreted in heuristics terms meaningful to potential practitioners. The second approach is preferable for its rigor and as an integrating enhancement to the engineering education experience. Unfortunately, the restrictions on available classroom time might not allow for a live in-class development without an efficient presentation and self-study guide such as is presented in the present paper. The present paper has been developed to overcome the time restriction by presenting detailed development of the ZTE in simple steps using some graphical tools included in the latest version of a popular equation editor. These used tools are colorization and special annotations to indicate cancellation and repositioning of terms. These very simple features should both clarify and accelerate the presentation. The result is a presentation that can be conducted in class without an excessive investment in time or be readily packaged into a video presentation for outside class student-paced self-study. To preview the proposed presentation, one begins as almost always with a sketch of the zone as control volume. Next the thermodynamic properties of the fluid are addressed. An important feature of this presentation is deferring the use of the usual psychrometric properties of moist air, which are based on the mass of dry air in the mixture, in favor of using the independent properties of the water vapor and the dry air. Both fluids are properly taken as ideal gases. Then mass conservation equations for the dry air and the water vapor are written. Next the time dependent energy equation of the zone is written with the usual observation that only the internal energy is important. With some careful considerations, these equations can be combined and then simplified. An important simplification comes from the observation that the pressure in a building zone is both inherently and controlled to be very nearly constant. An important finding is the interesting fact that, while the ZTE begins as an equation for the extensive internal energy, the constant pressure specific heat ultimately appears and multiplies the time derivative of temperature in the finalized form. Ultimately the ZTE can be also written in a form wherein the moist specific heats from psychrometrics appear naturally but rigorously. In its final form the ZTE can be compared with the ZTE reported to be used in EnergyPlus and minor differences in the moist specific heats can be seen as acceptable approximations. One apparent missing feature in the EnergyPlus version is a failure to model the cooling effect of evaporating liquid water in the conditioned space itself. In practice at least in commercial and institutional building, such evaporative cooling is usually accomplished in the HVAC system external to the space; consequently, this deficiency can and be should be circumvented. Ultimately, this presentation should be a useful addition to an intermediate thermodynamics course or an engineering course on thermal control of the built environment.

Citation
Format

Jeter, S., & fernandez, C. (2022, August), Presenting an Accessible yet Rigorous Development of the Zone Temperature Equation: An Important Thermodynamic Result Inherently Interesting and Educational Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--41306

TY - CPAPER
AB - The Zone Temperature Equation (ZTE) is a time-derivative equation of for the temperature of a building “zone”, which is a control volume representing a part or the whole of the conditioned space in a building conditioned for thermal environmental control. As such the ZTE is an important tool used in building energy systems simulations. The usual version of the equation is probably best stated in the references for EnergyPlus the widely used and generally well-regarded building energy simulation package. This program was developed as a major project supported by the US Department of Energy involving various national labs and contractors and with substantial participation by private industry. The resulting program is, with good reason, widely used around the world. Indeed, EnergyPlus appears to be the first popular building energy simulation program that is intended to be thermodynamically rigorous, in that many previous simulation programs were primarily hourly load calculations. Indeed, the ZTE, which represents combined energy and mass conservation, is presented along with conservation equations for moisture and carbon dioxide concentration in EnergyPlus. The ZTE in EnergyPlus can be shown to be accurate for its intended use; nevertheless, it has some theoretical deficiencies, one of which could have practical implications. Obviously, this equation is important for its role in such an important simulation and is interesting pedagogically in itself as being a rather ingenious combination of the mass and energy conservation principles.
Junior or senior students in mechanical or related engineering interested in building energy systems or related thermal systems should be aware of this equation, especially the rigorous and thermodynamically exact form presented in the present paper. Such students should have finished the usual first semester thermodynamics course and be well aware of energy and mass conservation as well as the properties of ideal gases. These are the only preparation needed to fully understand and appreciate and even apply the ZTE. For classroom presentation at this level, at least two approaches are feasible (1) the equation can be presented by quotation from the relevant reference material with some heuristic justification or (2) if time permits the equation can be developed from first principles and then interpreted in heuristics terms meaningful to potential practitioners. The second approach is preferable for its rigor and as an integrating enhancement to the engineering education experience. Unfortunately, the restrictions on available classroom time might not allow for a live in-class development without an efficient presentation and self-study guide such as is presented in the present paper.
The present paper has been developed to overcome the time restriction by presenting detailed development of the ZTE in simple steps using some graphical tools included in the latest version of a popular equation editor. These used tools are colorization and special annotations to indicate cancellation and repositioning of terms. These very simple features should both clarify and accelerate the presentation. The result is a presentation that can be conducted in class without an excessive investment in time or be readily packaged into a video presentation for outside class student-paced self-study.
To preview the proposed presentation, one begins as almost always with a sketch of the zone as control volume. Next the thermodynamic properties of the fluid are addressed. An important feature of this presentation is deferring the use of the usual psychrometric properties of moist air, which are based on the mass of dry air in the mixture, in favor of using the independent properties of the water vapor and the dry air. Both fluids are properly taken as ideal gases. Then mass conservation equations for the dry air and the water vapor are written. Next the time dependent energy equation of the zone is written with the usual observation that only the internal energy is important. With some careful considerations, these equations can be combined and then simplified. An important simplification comes from the observation that the pressure in a building zone is both inherently and controlled to be very nearly constant. An important finding is the interesting fact that, while the ZTE begins as an equation for the extensive internal energy, the constant pressure specific heat ultimately appears and multiplies the time derivative of temperature in the finalized form. Ultimately the ZTE can be also written in a form wherein the moist specific heats from psychrometrics appear naturally but rigorously.
In its final form the ZTE can be compared with the ZTE reported to be used in EnergyPlus and minor differences in the moist specific heats can be seen as acceptable approximations. One apparent missing feature in the EnergyPlus version is a failure to model the cooling effect of evaporating liquid water in the conditioned space itself. In practice at least in commercial and institutional building, such evaporative cooling is usually accomplished in the HVAC system external to the space; consequently, this deficiency can and be should be circumvented. Ultimately, this presentation should be a useful addition to an intermediate thermodynamics course or an engineering course on thermal control of the built environment.

AU - Sheldon Jeter
AU - christopher fernandez
CY - Minneapolis, MN
DA - 2022/08/23
PB - ASEE Conferences
TI - Presenting an Accessible yet Rigorous Development of the Zone Temperature Equation: An Important Thermodynamic Result Inherently Interesting and Educational
UR - https://peer.asee.org/41306
DO - 10.18260/1-2--41306
ER -