1. Study of forward and inverse airflow models for use in systematic design of indoor air sensor systems Y. Lisa Chen1,2 and Dr. Jin Wen2 1Koerner Family Foundation Fellow, 2Dept. of Civil, Architectural and Environmental Engineering, Drexel University
Forward airflow models
Computational Fluid Dynamics (CFD)
Provides detailed airflow and contaminant dispersion information
Requires specific knowledge of fluid dynamics and numerical techniques
Computationally intense
Multi-zone & Zonal models
Sub-divide zones into sub-zones
Zonal models different because of special subzones
Cannot provide detailed results but computationally efficient
Studies
Initial conditions
t=0, v=?,C=?
Boundary conditions
Using forward airflow models
Small zone 3.7x3.7x2.5 m with variations in:
Diffuser and exhaust location –typical layouts found in commercial offices
Furniture location – obstruction to airflow and contaminant dispersion
Airtightness level – infiltration of “clean” outdoor air
Simulated using 3 airflow models:
Multi-zone, Zonal, and CFD
Genetic algorithm (GA) determines possible sensor configurations
Objective functions: min detection time and min occupant exposure
Results
Data from simpler airflow models that included simple diffusers were able to design sensor systems capable of performing just as well as those designed using more accurate CFD models that included more complex diffusers;
Inclusion of furniture under exhaust positively affected dispersion of contaminants;
Inclusion of furniture under diffuser adversely affected dispersion of contaminants;
Inclusion of infiltration adversely affected dispersion of contaminants.
Using inverse airflow models for single zone
Small zone 3.0x3.0x2.7 m with variations in:
In lieu of experimental data, CFD velocity data provided to inverse model
Designing sensor systems
Pre-configured & optimized to maximize airflow estimation accuracy
Configuration (a) & (b) showed greatest improvement to airflow estimation accuracy over case with no sensors
Using GA, sensor info that provides greatest improvement to airflow estimation accuracy are:
Along wall, closest to outlet, measuring velocity in direction of bulk airflow, in this case, vertical direction
Using inverse airflow models for entire building
Three-zone commercial building
CO2 contaminant data simulated using multi-zone model for each zone under varying generation rates
Constrained linear least squares able to solve building airflow network given contaminant data & source generation rates under steady state conditions
Under transient (or data with error), constrained linear least squares fails
Forward through space and time
Inverse airflow models
Singular value decomposition (SVD)
Method to solve underdetermined system of equations
Solution:
ρ A v = b (1)
Normally solved v = 1/ρ A-1b (2)
A is underdetermined, so use SVD to find pseudo-inverse of A
A* = VΣ+UT (3)
Then, v = 1/ρ A*b (4)
Constrained linear least squares
Method to solve just- and over-determined systems
C Q = -S (1)
ΣQij - ΣQij = 0 (2)
Past
Present
Future
Backward through space and time
v1,C1
v2,C2
v3,C3
Contaminant dispersion
t = 60 sec
t = 180 sec
Systematic sensor system design
Release 1
Occupant 1 2
Future work 4 2
Sensor location designed using data from simpler airflow models
Sensor location designed using data from CFD model 3
Using forward airflow models – include more variations
Using inverse airflow models – include sensor uncertainty