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Rigorous mathematical formulation of net escape velocity and net escape probability determining a macroscopic
Naoki Ikegaya1, Kazuhide Ito1, Mats Sandberg2
1Faculty of Engineering Sciences, Kyushu University, Fukuoka, Japan.
Indoor Air
|July 29, 2022
Summary
This study provides precise mathematical formulas for Net Escape Velocity (NEV) and Net Escape Probability (NEP) in indoor air environments. These formulations offer a clearer physical interpretation and application for air quality assessment.
Area of Science:
- Indoor air quality
- Fluid dynamics
- Environmental engineering
Background:
- Net Escape Velocity (NEV) and Net Escape Probability (NEP) describe scalar discharge from indoor sources.
- Existing definitions lack precise mathematical formulation, hindering application.
Purpose of the Study:
- Derive rigorous mathematical formulations for NEV and NEP.
- Provide clear physical interpretations and applications for these concepts.
- Establish a basis for NEV as an air quality index.
Main Methods:
- Developed precise mathematical formulations for NEV and NEP.
- Solved diffusion and advection-diffusion equations numerically.
- Analyzed scalar flux and population behavior in control volumes.
Main Results:
- The diffusion problem showed only outgoing scalar flux.
- The advection-diffusion problem revealed a returning scalar population.
- Derived formulations clarify NEV's physical meaning and perfect escape conditions.
Conclusions:
- The derived mathematical formulations enhance the understanding of NEV and NEP.
- NEV can be applied as a robust air quality index with clear physical interpretation.
- This work clarifies scalar transfer probabilities in indoor environments.
Keywords:
indoor ventilationnet escape probabilitynet escape velocitypurging flow ratescalar concentrationtransfer probabilityMore Related Videos
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