Flow Control for Cooling of Turbine Blades

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Flow Control for Cooling of Turbine Blades

• IGERT Annual Workshop
• Luis Alvergue
• Electrical and Computer Engineering
• Advisors
• Dr. Guoxiang Gu
• Electrical and Computer Engineering
• Dr. Sumanta Acharya
• Mechanical Engineering

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Problem Statement

• The motivation for cooling turbine blades is a
  result of the environment where the turbine
  blades operate.
• Average environment temperature is higher than
  the melting point of the material that makes up
  the blades.
• If the blades are not cooled, they will melt.

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Proposed Solution

• Injecting cool air on the blades so that a film
  layer forms on the blades.

Fig 2 Gas Turbine Combustor
Fig 1 Blade Cross Section
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Proposed Solution

• Hotspots may occur consequently, the flow of
  cool air is not constant at all times.
• Active Flow Control may enhance cooling and
  eliminate hot spots.

Fig 3 A Modern Control System
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Interdisciplinary Approach

• Renaissance Approach 2
• Developments in control theory in the last few
  decades have expanded the available tools which
  may be applied to regulate physical systems.
• Flow Control application
• Takes into account the relevant flow physics used
  to design control algorithms.
• Conversely, takes into account the requirements
  and limitations of control algorithms when
  designing flow models.
• ''Renaissance'' approach tackles these problems
  with an interdisciplinary outlook.

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Interdisciplinary Approach

• Electrical Engineering
• Technology to model, simulate, and control the
  flow dynamics.
• Mechanical Engineering
• The research problem is stated in terms of the
  discretized Navier-Stokes equations and the
  physics associated with them.

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Model Based Control Theory in Fluid Mechanics

• Closed Loop Feedback Control
• In simple electrical or mechanical systems,
  equations for matrices with n2 unknowns (where n
  is the dimension of the state) can be easily
  managed.
• ODE discretizations of turbulent flow systems can
  easily have order n O(106).
• The most appropriate technique to reduce such
  system descriptions while still retaining their
  essential features is not obvious.
• Why reduce the system order?
• High order models take longer computation times
  for the simulations.
• This places a constraint on being able to control
  the system in real-time. For that reason, this
  model has to be reduced to a lower order one that
  will permit us to design a control strategy that
  is feasible to implement in a real-time.

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Current Work

• Modeling and Control of Flexible Structures in
  Frequency Domain
• Current drawbacks in the control area modeling
  and control are dealt with separately.
• There are some efforts on this issue by
  developing robust system identification and
  robust feedback control.
• However the modeling error resulted from system
  identification is quantified differently from the
  uncertainty that can be coped with by robust
  control.
• Hence we propose an integrated approach that
  unifies the modeling and control, which have the
  same quantification of the modeling error.
• The control algorithm is H-infinity loopshaping
  that is based on classical frequency domain
  design method developed by Bode and Nyquist.
• The uncertainty which can be tolerated by the
  H-infinity loopshaping method is in the form of
  gap metric difficult to minimize in modeling
  part.
• For modeling we presently employ curve fitting.
• Conditions are established for robust stability
  and performance.

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Current Work

• Modeling Simulation Results
• Kung's algorithm for a reduced order model.

Fig 4 Real model vs Reduced Order model
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Current Work

• Modeling Simulation Results
• Curve fitting algorithm for a reduced order model.

Fig 5 Real model vs Reduced Order model
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Current Work

• Control Simulation Results
• Robust control algorithm for a reduced order
  model.

Fig 6 Output Response
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Current Work

• Model Order Reduction of a Flow System

Fig 7 2D temperature distribution for an input
jet at location x-1
Fig 8 Model for Flow System
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References

• 1 BEWLEY, T.R. (2002) The emerging roles of
  model-based control theory in fluid mechanics
  Advances in Turbulence IX. Proceedings of the
  Ninth European Turbulence Conference.
• 2 BEWLEY, T.R. (2001) Flow control new
  challenges for a new Renaissance. Progress in
  Aerospace Sciences 37 200121-58.