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In this study, the results of a direct numerical simulation (DNS) of turbulent drag reduction by microfibers in a plane channel flow at a shear Reynolds number of Re = 950 are reported. For this purpose, we make use of a numerical solution of three-dimensional, time-dependent Navier-Stokes equations for the incompressible turbulent flow of a non-Newtonian fluid. The non-Newtonian stress tensor which is required to solve the problem depends on the orientation distribution of the suspended fibers, which is computed by a recently-proposed algebraic closure model. It is shown that the use of this algebraic closure, due to the great reduction in computational efforts, enables us to perform a DNS at high Reynolds numbers. Ultimately, statistical quantities of turbulence (in particular, the mean velocity profile, Reynolds stresses, etc.) are presented and discussed. Variations in the isotropy of the Reynolds stress tensor are explained by the aid of Lumley anisotropy map.

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In this study, a new method for producing initial conditions that are required for the Brownian dynamics simulation of dilute polymer suspension flows is proposed. For this purpose, the equilibrium probability distribution function is employed to generate an equilibrium ensemble of polymers. This approach is programmed and by using it, a polymer suspension in the inception of a simple shear flow is simulated. Also, the results of simulations in a similar flow configuration based on the conventional approach of generating initial conditions are presented. The excellent agreement between the results demonstrates the high accuracy of the proposed method for generating initial conditions. The main advantage of the proposed method is its low computational cost.

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In this study, using the results of a DNS of drag-reduced turbulent channel flow, vortical flow structures especially in the near-wall region are investigated. For this purpose, a Lagrangian Monte-Carlo method has been used to simulate the spatial orientation of fibers. Namely, the flow field is treated in an Eulerian manner whereas the fiber dynamics is described by a Lagrangian point of view. This method yields the exact solution of the governing equations. Vorticity fluctuations in the channel are studied and it turns out that the level of these fluctuations decreases in the drag-reduced flow. The reason for this reduction is explained using the reduction in velocity gradient fluctuations. Also, the distribution of the angle between the vorticity axis and the wall is studied and it turns out that horseshoe vortices exist in both flows. However, in the drag-reduced flow, they are formed farther away from the wall which indicates a weakening of sweep and ejection mechanism in the vicinity of the wall. This weakening leads to drag reduction. Also, the orientation of vortices in the drag-reduced flow is well ordered.

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In this study, the stochastic field method is developed for the direct numerical simulation of turbulent drag reduction by microfibers. For this purpose, the governing equations without any simplification are discretized on an Eulerian grid. A fifth-order upwind scheme is used for the discretization. A Monte-Carlo method is employed in the conformation space. Then, three-dimensional, time-dependent Navier-Stokes equations for the incompressible flow of a non-Newtonian fluid are numerically solved for a turbulent channel flow. Statistical quantities obtained by the proposed method are compared with those of a Lagrangian method and the high precision of the new method is demonstrated. The main advantage of the new method is its low computational cost.

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In this paper, a new algebraic closure model for the DNS of turbulent drag reduction in a channel flow using microfiber additives is presented. This model is an extension of an existing model and cures some the shortcomings of the old model. In the proposed model, using the velocity correlation tensor in the modeling process, more physical conditions of the flow field are taken into account. With this, some of the shortcomings of other models are cured. The proposed model is used to directly simulate turbulent drag reduction in a horizontal channel flow under the action of a constant pressure gradient. For this purpose, time-dependent, three-dimensional Navier-Stokes equations for the incompressible flow of a non-Newtonian fluid are numerically solved. Statistical quantities of obtained by the new model are compared with the results of previous simulations. The good agreement between the results demonstrates the proper accuracy of the new model. Especially, the root-mean-square of velocity fluctuations in the streamwise direction is predicted with high accuracy as compared to previous models. Other statistical quantities are also computed with appropriate accuracy. This model is capable of prediction all properties of a microfiber-induced drag-reduced flow.

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In this paper, a method for distributed control of nonlinear Burger’s equation is proposed. In this method, first the nonlinear partial differential equation governing the system is transformed into two linear partial differential equations using the Takagi-Sugeno linearization; such that their fuzzy composition exactly recovers the original nonlinear equation. This is done to alleviate the aliasing phenomenon occuring in nonlinear equations. Then, each of the two linear equations is converted to a set of ordinary differential equations using the fast Fourier transform (FFT). Thus, the combination of Takagi-Sugeno method and FFT technique leads to two ordinary differential equation for each grid point. For the stabilization of the dynamics of each grid point, the use is made of the parallel distributed compensation method. The stability of the proposed control method is proved using the second Lyapunov theorem for fuzzy systems. In order to solve the nonlinear burger equation, a combination of FFT and finite difference methodologies is implemented for the . Simulation studies show the performance of the proposed method, for example the smaller settling time and overshoot and relatively robustness with respect to the measurement noises.

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A semi-analytical method so-called the Scaled Boundary Finite-Element Method (SBFEM) is employed for solving two-dimensional steady-state reaction-diffusion equation with constant diffusion and decay coefficients which is widely used in contaminant transfer, chemical engineering and heat transfer problems. This method has been successfully applied to various problems of engineering such as elastodynamics, fracture mechanics and seepage. This method has advantages of both boundary element method and finite-element method. Only the boundary is discretized reducing the spatial dimension by one. Unlike the boundary element method no fundamental solution is required. Interpolation over the boundaries is approximated using shape functions same in the finite-element method. Singularities, anisotropic problems, non-homogeneities satisfying similarity and radiation condition at infinity used in modeling unbounded domains are simply modeled by this technique. In this study, after derivation of the scaled boundary finite-element formulations for reaction–diffusion equation, solution procedures based on dynamic-stiffness matrix are proposed. The accuracy and performance of the SBFEM is evaluated using numerical examples. There are a reasonable agreement between the results of the scaled boundary finite-element method, the analytical solutions and the popular numerical approaches.

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In this paper, a method for distributed control of temperature distribution in a thick rectangular functionally graded plate is proposed. In this way, the linear nonhomogenous conduction which its governing dynamics is a linear partial differential equation (PDE) with spatially varying coefficients is considered and actively controlled. For this purpose, firstly, this PDE is converted into a set of ordinary differential equations (ODEs) using the modified wavenumber methodology. This apporach is based on the combination of the fast Fourier transform (FFT) and finite difference techniques. Secondly, in order to stabilize each of these ODEs, linear optimal state feedback controller is utilized by minimizing a predefined performance index. The proposed controller is modified by adding a feedforward term to have a good tracking performance for the proposed method. The designed control inputs which are in the Fourier domain, are transfers to physical domain using the inverse Fast Fourier transform (IFFT). In order to solve the linear nonhomogenous conduction heat equation, a combination of finite difference and Runge-Kutta methodologies is implemented. Simulation studies show the performance of the proposed method, for example the smaller settling time, overshoot and also steady-state error.