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Optimal control of diffuser shapes for non-uniform flow.

G P Benham1, I J Hewitt1, C P Please1

  • 11Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG UK.

Journal of Engineering Mathematics
|April 2, 2019
PubMed
Summary

Optimal diffuser shapes balance widening and narrowing to maximize pressure recovery in non-uniform flows. This research identifies shapes that improve performance by considering wall drag and flow behavior.

Keywords:
DiffusersFluid dynamicsMathematical modellingOptimal controlShape optimisationTurbulence

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Area of Science:

  • Fluid dynamics
  • Aerodynamics
  • Computational fluid dynamics

Background:

  • Diffusers are crucial components in fluid systems for pressure recovery.
  • Non-uniform inflow conditions significantly impact diffuser performance.
  • Optimizing diffuser shape is essential for enhancing aerodynamic efficiency.

Purpose of the Study:

  • To identify optimal diffuser shapes that maximize pressure recovery under various non-uniform inflow conditions.
  • To investigate the trade-offs between flow acceleration and wall drag in diffuser design.
  • To develop a simplified model for predicting diffuser performance with complex flow profiles.

Main Methods:

  • Utilized a reduced mathematical model based on integrated mass and momentum equations.
  • Employed an optimal control problem framework with diffuser shape as the control variable.
  • Applied numerical optimization and Pontryagin's maximum principle for analytical solutions.
  • Investigated three classes of non-uniform inflow: distinct speed streams, similar speed streams, and linear shear profiles.

Main Results:

  • Optimal diffuser shapes balance early widening to manage flow acceleration and delayed widening to minimize wall drag.
  • The study identified specific optimal shapes for different non-uniform inflow profiles.
  • Piecewise linear approximations effectively represent optimal diffuser shapes, suggesting simplified design parameters.

Conclusions:

  • The findings provide insights into designing efficient diffusers for non-uniform flow conditions.
  • Simplified, parameterized diffuser shapes can be used for further analysis with advanced turbulence models.
  • This research contributes to the development of more efficient fluid dynamic systems.