# 使用形状优化和拓扑优化设计特斯拉微阀

2019年 11月 15日

### 特斯拉阀的机理

\mathrm{Di}= \frac{\Delta p_{\leftarrow}}{\Delta p_{\rightarrow}},

\mathrm{Re}=\frac{U_\mathrm{in}D\rho}{\mu},

### 在 COMSOL Multiphysics® 中进行拓扑优化

{F}_\mathrm{Darcy}
，其定义为

\mathbf{F}_\mathrm{Darcy}
= -\alpha(\theta_c)\mathbf{u},

### 对特斯拉微阀进行形状优化

COMSOL Multiphysics® 软件支持基于梯度的形状优化，通过固定网格拓扑结构来实现，即只改变网格节点的位置。从 COMSOL Multiphysics 5.5 版本开始，优化模块内置了多个形状优化特征功能，多项式边界 特征就是其中之一。该特征通过平滑方程处理内部节点的变形，而内壁的变形由以下公式给出

\mathbf{d}= \sum_i^n B^n_i(s)\mathbf{c}, \quad -d_\mathrm{max} \leq c_i \leq d_\mathrm{max},

Bernstein 多项式满足其系数在整个直线上的界限，这意味着直线上的每个点都被限制在一个边长为 2d_\mathrm{max} 的正方形盒子里移动。

### 参考文献

Valvular Conduit, Nicola Tesla, 1920, US Patent 1,329,559.

#### 评论 (5)

##### Hua Li
2023-07-24

May i ask you a question? i make a try to topology-optimize a kind of heat-exchanger(heat conduction coupling laminar flow),but in my topology-optimized result, the liquid domain didnt connect with each other,even the inlet is full of solid material. im confused, have you ever encountered such a problem？how to deal with it?

##### Kristian Ejlebjærg Jensen
2023-07-24 COMSOL 员工

You probably chose interpolation functions which caused that design to become a (local) optimum. It is possible that you can benefit from taking a look at https://www.comsol.com/model/98011.

##### Hua Li
2023-07-25

Thanks so much for your reply, I will take a look at the case and check my settings again.

##### Hua Li
2023-07-25

Another question, please, I also want to extend this kind of topology-optimization to 3D problem. Have you ever topology-optimized the heat conduction coupling laminar flow with COMSOL? Or maybe you use other tools?

##### Kristian Ejlebjærg Jensen
2023-07-25 COMSOL 员工

I am a COMSOL employee, so I do not use other tools. https://www.comsol.com/model/98011 performs topology optimization of heat conduction coupled to laminar flow in 2D. Extension to 3D is conceptually trivial, but in practice one has to use iterative solvers, possibly on a cluster.