Abstract. This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for some given cost functionals. The first one is to use the Piola transformation and derive the state derivative and its associated adjoint state; the second one is to use the differentiability of a minimax formulation involving a Lagrangian functional with a function space parametrization technique; the last one is to employ the differentiability of a minimax formulation with a function space embedding technique. Finally we apply a gradient type algorithm to our problem and numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.

This paper investigates the drag minimization in a two-dimensional flow which is governed by a nonhomogeneous Navier-Stokes equations. Two approaches are utilized to derive shape gradient of the cost functional. The first one is to use the shape derivative of the fluid state and its associated adjoint state; the second one is to utilize the differentiability of a minimax formulation involving a Lagrange functional with a function space parametrization technique. Finally, a gradient type algorithm is effectively formulated and implemented for the mentioned drag minimization problem.

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain for a given cost function is established by using the differentiability of a minimax formulation involving a Lagrangian functional combining with function space parametrization technique or function space embedding technique. We apply an gradient type algorithm to our problem. Numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible.

The ultra-fine dry powder injection process in non-pressure-accumulated and handheld fire extinguishers involves gas-phase and solid-phase two-phase movement. The fire-extinguishing effect is closely related to its jet form. In order to study the jet form accurately, this paper selects the discrete particle model, combines the advantages of Lagrange method and Euler method, and uses CFD simulation software FLUENT to numerically simulate the gas-solid two-phase jet shape of a nonpressure-accumulated and handheld fire extinguisher. And compares the simulation results with the experimental results, analyzes the flow field characteristics inside and outside the cylinder. The results show that the numerical simulation agrees well with the experimental results and can better represent the motion state of the two-phase flow. The numerical simulation results show that the duration of extinguishing agent particles injection is 1.07s, which is very close to the actual injection duration of 1.13s. The difference between the two is 4.4%. Within the acceptable error range, it is further proved that the simulation results are good agreements with the experiment.

No abstract