Ashdown, Minnie;
(2024)
A Stochastic Differential Equation model for natural air exchange in unoccupied buildings.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
Natural air exchange in buildings is a challenging construct to quantify, yet is crucial to understanding internal air quality and building energy efficiency. Techniques that attempt to resolve the equations of motion for fluids are typically highly computationally intensive, and require detailed models for individual settings. Empirical measurement techniques typically rely on time averaging and assumptions about the properties of the fluid within the measured space, and environmental conditions outside the building. However, this limits the representativeness of the measurement results, making it hard to understand variability of air exchange within the building and between different buildings (in time and space). This thesis develops a novel mathematical approach to air exchange rates, that can utilise empirical data to understand their dynamics in unoccupied naturally ventilated buildings. On the basis of CO2 time series represented as Itô diffusion processes, and linked through a change of measure, it is possible to leverage the relationship of the timeseries dynamics themselves, via their associated operator, to the Partial Differential Equation (PDE) representations used in contaminant transport problems. It is therefore possible to formulate a transport equation representing the contribution of the external dynamics of the CO2 timeseries to the internal dynamics, which in turn facilitates a characterisation of the “relative” residence time distribution within the space, and the distribution of air exchange rates. To test the theory, CO2 timeseries data was collected in an intermittently occupied dwelling in Cambridgeshire and fitted to the model. Although empirical results and validation are limited to a single case study, PDE solutions and associated air exchange rates are found to be a promising comparator to those obtained using conventional measurement techniques, and furthermore offer a much richer description of building air exchange rates and internal conditions experienced by occupants.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | A Stochastic Differential Equation model for natural air exchange in unoccupied buildings |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2024. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of the Built Environment > Bartlett School Env, Energy and Resources |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10202609 |
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