Shape Optimization of a Body Immersed in the Navier-Stokes Flow

2011 ◽  
Vol 80-81 ◽  
pp. 774-778
Author(s):  
Xian Bao Duan ◽  
Xin Qiang Qin ◽  
Ya Qin Guo
Keyword(s):  
Shape Optimization ◽  
Adjoint Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Shape Sensitivity ◽  
Navier Stokes Equations ◽  
Cost Functional ◽  
Drag Forces ◽  
Stokes Fluid ◽  
The Cost

In this study, we restrict our attention to shape optimization of a body immersed in the Navier-Stokes fluid flow. The formulation and numerical results of the proposed method are presented. The proposed method is based on an optimal control theory. The optimal state is defined by the reduction of drag forces subjected to the immersed object. The cost functional should be minimized is governed by the Navier-Stokes equations. The shape sensitivity analysis of the cost functional was derived based on the adjoint method. Finally, a numerical example is given to show the feasible for the proposed algorithm.

scholarly journals Shape optimization of a Helmholtz resonator using an adjoint method

2017 ◽  
Vol 9 (4) ◽  
pp. 394-408 ◽  
Author(s):  
Faisal Caeiro ◽  
Carlo Sovardi ◽  
Kilian Förner ◽  
Wolfgang Polifke
Keyword(s):  
Shape Optimization ◽  
Acoustic Impedance ◽  
Optimization Problem ◽  
Adjoint Method ◽  
Stokes Equations ◽  
Helmholtz Resonator ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Direction ◽  
Objective Functional

This paper proposes a method for shape optimization in aero-acoustics and applies it to a Helmholtz resonator. The objective is to realize a desired acoustic impedance by optimizing the shape of the neck of the resonator, in due consideration of the excitation level. The optimization problem is formulated with a suitable objective functional, where the Navier–Stokes equations act as a partial differential equation (PDE) constraint in a Lagrangian functional. By exploiting the understanding of the relevant flow physics, it is possible to formulate the objective functional in the time domain, although the optimization target, i.e. the acoustic impedance, is a quantity defined in the frequency domain. This optimization problem is solved by a gradient-based optimization. The shape gradient of the objective functional is determined by an adjoint method, which requires solving two sets of PDEs in time: the so-called forward and backward problems. The forward problem is represented by the Navier–Stokes equations and is solved in the positive time direction. The set of equations for the backward problem, which has to be solved in the negative time direction, is derived in the current study. From the solutions of the forward and backward problems, the shape derivative for the current optimization step is calculated. Iterative optimization steps then bring the impedance to the target value.

Discussion on Clustering Effects in Vertical Gas-Particle Flows

2000 ◽  
Author(s):  
Eivind Helland ◽  
Rene Occelli ◽  
Lounes Tadrist
Keyword(s):  
Gas Phase ◽  
Stokes Equations ◽  
Lagrangian Approach ◽  
Inelastic Collisions ◽  
Navier Stokes ◽  
Coupling Term ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Drag Forces ◽  
Particle Flows

Abstract Simulations of 2D gas-particle flows in a vertical riser using a mixed Eulerian-Lagrangian approach are addressed. The model for the interstitial gas phase is based on the Navier-Stokes equations for two-phase flow with a coupling term between the gas and solid phases due to drag forces. The motion of particles is treated by a Lagrangian approach and the particles are assumed to interact through binary, instantaneous, non-frontal, inelastic collisions with friction. In this paper different particle clustering effects in the gas-particle flow is investigated.

scholarly journals Unstructured Adjoint Method for Navier-Stokes Equations

2005 ◽  
Vol 48 (2) ◽  
pp. 202-207 ◽  
Author(s):  
Hyoung-Jin KIM ◽  
Kazuhiro NAKAHASHI
Keyword(s):  
Adjoint Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical Investigation of the Effect of Balancing-Hole on the Axial Force of a Partial Emission Pump

2014 ◽  
Author(s):  
Zhang Lisheng ◽  
Jiang Jin ◽  
Xiao Zhihuai ◽  
Li Yanhui
Keyword(s):  
Axial Force ◽  
Stokes Equations ◽  
Dominant Role ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Design Parameters ◽  
Navier Stokes Equations ◽  
Computational Fluid Dynamics Cfd ◽  
The Cost

In this paper numerical simulations were conducted to analyze the effects of design parameters and distribution of balancing-hole on the axial-force of a partial emission pump. The studied pump is a single stage pump with a Barske style impeller. Based on the original impeller, we designed 7 pumps with different balancing-hole diameters and the partial emission pump equipped with different impellers were simulated employing the commercial computational fluid dynamics (CFD) software Fluent 12.1 to solve the Navier-Stokes equations for three-dimensional steady flow. A sensitivity analysis of the numerical model was performed with the purpose of balancing the contradiction of numerical accuracy and the cost of calculation. The results showed that, with increasing of the capacity, the axial force varies little. The diameter of the inner balancing-hole plays a dominant role of reducing axial-force of partial emission pump, the axial-force decreases with increasing of inner balancing-hole diameter on the whole range of operation, the axial-force of impeller without inner balancing-hole is approximately 3 times larger than that of impeller with inner balancing-hole. While the diameter of outer balancing-hole has a reverse effects compared with that of inner balancing-hole. With increasing of outer balancing-hole, the axial force increases accordingly.

scholarly journals On three-dimensional incompressible Navier-Stokes fluid on cantor sets in spherical Cantor type co-ordinate system

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 853-858
Author(s):  
Zhi-Jun Meng ◽  
Yao-Ming Zhou ◽  
Dong-Mu Mei
Keyword(s):  
Heat Conduction ◽  
Stokes Equations ◽  
Heat Conduction Problem ◽  
Three Dimensional ◽  
Cantor Sets ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Fluid ◽  
Incompressible Navier Stokes Equation

This paper addresses the systems of the incompressible Navier-Stokes equations on Cantor sets without the external force involving the fractal heat-conduction problem vial local fractional derivative. The spherical Cantor type co-ordinate method is used to transfer the incompressible Navier-Stokes equation from the Cantorian co-ordinate system into the spherical Cantor type co-ordinate system.

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