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

Results and Discussion

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)

First 4 POD Modes Re 250

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

Single Re Heuristic Method

§  Place Sensors at the peaks of the spatial Modes:

Sensors

1st Mode Re 200 vs. Re 350

Peak Shift as f(Re)

§  Peaks shift upstream and closer to centerline as Re increases

4 Sensors at Mean Locations

4 Sensors Upstream Locations

4 Sensors Downstream Locations

Estimation Errors

Results and Discussion

Sensor configuration errors for CFD data

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