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