Optimum design of minimum drag bodies in incompressible laminar flow using a control theory approach
Optimum design of minimum drag bodies in incompressible laminar flow using a control theory approach
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使用控制理论方法优化不可压缩层流中最小阻力体的设计
DOI：
10.1080/174159794088027570
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
V. Modi
中科院分区：
文献类型：
--
作者：
J. Huan;V. Modi
研究了在保持截面面积(单位跨度体积)不变的情况下，改变二维体的形状以减小其阻力的问题。采用定常N-S方程描述的二维不可压缩层流流动。本文得到了一组“伴随”方程，它的解允许计算导致较低粘性阻力的物体外形变化的方向和相对大小。得到了Dirichlet型远场条件下偏微分方程组的正解和伴随解。用上述边界条件对这两组方程的每个解重复修改身体形状，将导致指定截面区域的身体具有最小阻力。对于这样的物体，剪切和“伴随”剪切的乘积在物体的各处都是恒定的。即使在直接方程和伴随方程中保留了粘性项，在或。
The problem of modifying the shape of a two-dimensional body to reduce its drag while maintaining its section area (volume per unit span) constant is addressed. Two-dimensional, incompressible, laminar flow governed by the steady-state Navier-Stokes equations is assumed about the body. In this paper, a set of “adjoint” equations is obtained, the solution to which permits the calculation of the direction and relative magnitude of change in the body profile that leads to a lower viscous drag. The direct as well as the adjoint set of partial differential equations are obtained for Dirichlet-type far-field conditions. Repeatedly modifying the body shape with each solution to these two sets of equations with the above boundary conditions, would lead to a body with minimum drag, for a specified section area. For such a body it is shown that the product of shear and the “adjoint” shear is constant everywhere along the body. Even though the viscous terms are retained in the direct and the adjoint equations, in or...