^{®}, from Friendship Systems GmbH.

Design constraints are enforced during optimization for practical reasons such as keeping the cross-sectional shape and area constant, fixing the inlet positions and vertical location of outlet and keeping the main channel length under 2.5 mm.

The mixing criterion (objective function) is based on the average deviation, σ, which is given by

$latex \displaystyle \text{ }\!\!\sigma\!\!\text{ }=\text{ }\!\!~\!\!\text{ }\left\langle {{{{\left( {\text{C}-\text{ }\!\!~\!\!\text{ }\left\langle C \right\rangle } \right)}}^{2}}} \right\rangle$

where C is the concentration of any of the fluids at the outlet and <^{.}> means the average of the quantity inside. $latex \displaystyle \text{ }\!\!\sigma\!\!\text{ }=0.0$ means 100% mixing and $latex \displaystyle \text{ }\!\!\sigma\!\!\text{ }=0.5$ means no mixing at all. Therefore, the objective of the design optimization is to bring the value of $latex \sigma $ as close to zero as possible.

Parameters | Baseline Design | Best Design |

inlet length | 5.0 | 4.0 |

junction length | 5.0 | 2.0 |

junction angle | 20.0 | 85.0 |

mid length | 8.5 | 14.1 |

mid angle | 0.0 | 41.9 |

outlet length 1 | 1.0 | 1.0 |

outlet length 2 | 3.5 | 2.9 |

outlet angle | 0.0 | 29.9 |

outlet X shift | 7.0 | 4.0 |

Objective function | 0.051 | 0.047 |

Whether performing a parametric study for sediment scour, a microchannel geometry optimization, or a metal casting part (that I will discuss in a future blog), design optimization has many applications. ** FLOW-3D’s **seamless integration with CAESES offers a powerful solution for optimization studies in a very hands-off manner, saving time and producing better designs.

Learn more about the power and versatility of modeling microfluidic applications with **FLOW-3D***.*

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