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Research Papers: Fundamental Issues and Canonical Flows

Direct Simulation Based Model-Predictive Control of Flow Maldistribution in Parallel Microchannels

[+] Author and Article Information
Mathieu Martin, Chris Patton, John Schmitt

School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331

Sourabh V. Apte1

School of Mechanical, Industrial and Manufacturing Engineering, Oregon State University, Corvallis, OR 97331sva@engr.orst.edu

1

Corresponding author.

J. Fluids Eng 131(11), 111201 (Oct 08, 2009) (17 pages) doi:10.1115/1.3216519 History: Received February 17, 2009; Revised July 17, 2009; Published October 08, 2009

Flow maldistribution, resulting from bubbles or other particulate matter, can lead to drastic performance degradation in devices that employ parallel microchannels for heat transfer. In this work, direct numerical simulations of fluid flow through a prescribed parallel microchannel geometry are performed and coupled with active control of actuated microvalves to effectively identify and reduce flow maldistribution. Accurate simulation of fluid flow through a set of three parallel microchannels is achieved utilizing a fictitious-domain representation of immersed objects such as microvalves and artificially introduced bubbles. Flow simulations are validated against experimental results obtained for flow through a single high-aspect ratio microchannel, flow around an oscillating cylinder, and flow with a bubble rising in an inclined channel. Results of these simulations compare very well to those obtained experimentally, and validate the use of the solver for the parallel microchannel configuration of this study. System identification techniques are employed on numerical simulations of fluid flow through the geometry to produce a lower dimensional model that captures the essential dynamics of the full nonlinear flow, in terms of a relationship between valve angles and the exit flow rate for each channel. A model-predictive controller is developed, which employs this reduced order model to identify flow maldistribution from exit flow velocities and to prescribe actuation of channel valves to effectively redistribute the flow. Flow simulations with active control are subsequently conducted with artificially introduced bubbles. The model-predictive control methodology is shown to adequately reduce flow maldistribution by quickly varying channel valves to remove bubbles and to equalize flow rates in each channel.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Schematic of parallel microchannels with bubbly flow

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Figure 2

Schematic of material volumes for a circular object

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Figure 3

Schematic of the variable storage in time and space: (a) time-staggering, (b) three-dimensional variable storage, (c) cv and face notation, and (d) index notation for a given k-index in the z direction. The velocity fields (ui and uN) are staggered in time with respect to the volume fraction (Θ), density (ρ), particle position (Xi), the pressure field (p), and the rigid body force (fi,R). All variables are collocated in space at the centroid of a control volume except the face-normal velocity uN, which is stored at the centroid of the faces of the control volume.

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Figure 4

Model-predictive control scheme: (a) inputs and outputs and their relation to the control and prediction horizon’s (b) control system diagram including the model-predictive controller

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Figure 5

Schematic of CFD-controller interface

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Figure 6

Schematic and grid for the single channel geometry. The grid used consists of around 1.5×106 grid elements. Only a small section of the grid is shown.

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Figure 18

Temporal evolution of the bubble motion and the controller commands: (a) controller command —– history correlated with angular location – – – – for each microvalve, (b): axial — and vertical – – – – velocities of the bubble, and (c) axial —– and vertical – – – – locations of the bubble. Time is expressed in milliseconds, velocities are expressed in m/s, bubble locations are expressed in millimeters, and angles are expressed in degrees.

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Figure 19

Pressure contours in the presence of two bubbles before the controller is activated. The pressure is expressed in pascals and lengths are in millimeters.

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Figure 20

Temporal histories of controller command, mass-flow rates, and forces on the bubbles: (a) history of controller commands — correlated with angular positions of microvalves – – – ; (b) mass-flow rates measured at the end of each channel:— shows the top channel, – – – shows the middle channel, and –⋅–⋅– shows the bottom channel; (c) history of total forces acting on the bubbles: — shows the bubble initially in the top channel, and – – – shows the bubble initially in the bottom channel. Time is expressed in milliseconds, angles are expressed in degrees, force is expressed in μN, and mass-flow rates are expressed in kg/s.

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Figure 21

Temporal evolution of velocity contours and bubble trajectories in the coupled CFD-controller simulation for two bubbles. The lengths are expressed in millimeters, and the velocity is expressed in m/s.

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Figure 7

Velocity profiles in the center plane of the channel taken at x′=1 cm and x′=10 cm from the entrance of the channel. ● shows the experimental data, – – – shows the numerical simulation from Ref. 24, and — shows the present study. The velocity is expressed in m/s and the y location is expressed in microns.

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Figure 8

Velocity distribution along the central line of the channel. Re=196: ▲ shows the experimental data from Ref. 24, and — shows the present simulation; Re=1895: ▼ is the experimental data, and – – – shows the present simulation. Velocity is expressed in m/s and the x location is expressed in meters.

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Figure 9

Normalized axial velocity (u/Um) at three different phase positions. The velocity is measured at a fixed x location (x=−0.6d) relative to the initial location of the particle center: ◻ shows the experimental data from Ref. 25, — shows the present simulation, and – – – shows the numerical results from Ref. 27.

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Figure 10

Comparison of experimental ● and numerical simulations – – – (26) with the current simulation —. (a) shows the particle trajectory inside the domain (the –⋅– line shows the initial trajectory due only to the effect of gravity), (b) shows the velocity of the particle in the lateral direction, and (c) shows the velocity on the vertical direction. The particle position is expressed in meters and the velocities are expressed in m/s.

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Figure 11

Temporal evolution of a spherical bubble rising in a water column: U∗=U/Uterminal and t∗=t/τ95. Square symbols are for Ref. 28 and circle is for the present simulation.

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Figure 12

Steady state velocity contours in a parallel microchannel after flow rates in each channel are made equal. Also shown are the steady-state position of the microvalves. Lengths are expressed in millimeters and the velocity contours are in m/s.

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Figure 13

Time evolution of the flow rates (a) and controller input (b) to the flow solver: – – – shows the data for the top channel; — shows the middle channel; – – shows the bottom channel. The mass-flow rate is expressed in kg/s, time is expressed in milliseconds, and angles are expressed in degrees.

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Figure 14

Velocity and pressure contours inside the parallel microchannel with presence of a stationary bubble in the top channel. The lengths are expressed in millimeters, the velocity is expressed in m/s, and the pressure is expressed in pascals.

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Figure 15

Temporal evolution of mass-flow rate (a) in each channel and steady-state pressure drops (b) in each branch: — shows the top channel; – – – shows the middle channel; – – – shows the bottom channel. The mass-flow rates are expressed in mg/s, time in milliseconds, length in millimeters, and pressure in bars. The dashed rectangle in right panel represents the location of the bubble.

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Figure 16

Temporal evolution of the total force acting on the bubble: – – – shows that all channels are open, and — shows that the middle and bottom channels are completely closed. The forces are expressed in μN and the time is expressed in milliseconds. The horizontal dashed line represents the threshold inertial force necessary to set the bubble in motion.

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Figure 17

History of the flow in each channel with injection of the bubble at t=0.04 ms. — shows the data for the top channel; – – – shows the middle channel; – – shows the bottom channel. The time is expressed in milliseconds and the mass-flow rate is expressed in mg/s.

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