Post on 13-May-2023
Aeronautics Research Center – US Air Force Academy
POD Based Sensor Placement in a D-shaped Cylinder Wake at Varying
Reynolds Numbers APS DFD Meeting 2004
Seattle, WA
Stefan Siegel Kelly Cohen
Thomas McLaughlin
Outline § Introduction and Background
– Cylinder Wake Feedback Control – Controller Design and Approach
§ CFD and Experimental Setup – Water Tunnel Experiment – CFD Simulation – Proper Orthogonal Decomposition
§ Results – Single Re Sensor Placement Heuristics – Problems in sensing for varying Re – Estimation Quality Results
§ Conclusions
Cylinder Wake Feedback Control
Actuation
Controller
Sensors
steady
unsteady
Sketches from: Munson, Young, Okiishi. Fundamentals of Fluid Mechanics. p 601.
Develop a closed-loop control strategy to suppress the Karman vortex street of a D shaped Cylinder at Reynolds numbers of 100
Control Strategy
Mode Estimator
(LSE)
Sensors
Sensor Information (Velocity, Pressure)
Flow Modes (POD Amplitudes)
PD Controller (acts on
POD Mode 1)
Actuator Command (Displacement, Velocity)
Actuator
Low Pass Filter
Fc = 4*Fn
Experimental Geometry § D-shaped Body Model
– Semi-Ellipse AR 140:8 – Base height H – 7 mm – Span – 380 mm – Length – 61.25 mm
§ Switch to D-shaped geometry because: – It provides a fixed separation point – More internal room to implement
actuators – Blowing and suction actuators
instead of translation
Computational Grid
2D Simulation, ~200k Grid points, unstructured
250 time steps per shedding cycle
POD Domain
POD
POD (Proper
Orthogonal Decomposition)
N Spatial Modes M1_U(x,y) M1_V(x,y)
M2_U(x,y)
.... MN_V(x,y)
K Temporal Mode Amplitudes
A1(t) A2(t) …
AN(t)
N Snapshots of Flow Field
U(x,y,t) V(x,y,t)
Goal § Estimate the mode amplitudes for the first
two modes (>90% of the energy) to better than 10% error
§ Find fixed sensor locations for a range of Re that accomplish this
§ Use as few sensors as possible
Results and Discussion § For a given sensor configuration the
estimation error is typically higher for higher Reynolds numbers (why?)
§ Therefore sensor configurations that are optimized for higher Re deliver overall better quality estimates
§ Using four sensors, the best sensor configuration yielded less than 10.6% estimation error at all Re – acceptable for most controllers
Results and Discussion § Doubling the number of sensors to 8 results
in estimation errors of 5.2% or better for all Reynolds numbers – or less than half of the best 4 Sensor configuration
§ For the optimal 4 Sensor configuration, the maximum error encountered for all Re is about twice that of a sensor configuration optimized for a single Re
Conclusions § We found a sensor placement scheme
using four sensors that was able to accurately estimate temporal mode amplitudes for a large range of Reynolds numbers
§ These sensor placement schemes were evaluated using CFD data and PIV data
§ This indicates that the heuristic sensor placement strategy is suitable to estimate flow fields of varying Re