This paper proposes a new acceleration gradient method by addition of the Taylor expansion and conjugate direction to Nesterov’s acceleration gradient method. It was validated by updating the oil film thickness to minimize the friction coefficient on a textured surface. Nesterov’s acceleration gradient method converges faster than the gradient method for classical first-order optimization methods. The Taylor expansion of this mathematical technique reaches a more accurate approximation by incorporating higher-order terms. The conjugate direction is used in large-scale problems because it offers better convergence than the gradient descent method and is less memory-intensive than the Newton method. We introduced these into Nesterov’s acceleration gradient method to improve the convergence rate. The gradient of the design variable was obtained by the adjoint variable method. The results demonstrate the proposed method to converge faster than Nesterov’s accelerated gradient method. All the numerical calculations were performed by the finite element method using FreeFEM++.
This study provides detailed information on the pressure distribution inside a pipe with a continuous longitudinal slot, theoretically investigating the parameter dependency of the pressure distribution on the design parameters of the pipe: Reynolds number at the inlet, aspect ratio of the pipe, slot width, and pressure loss coefficient of the slot. The flow through a pipe with a continuous longitudinal slot is theoretically modeled in one dimension. The model follows the mass and energy conservation laws and considers the pressure loss at the slot. The results show that depending on the aspect ratio of the pipe and the Reynolds number at the inlet, the pressure distribution inside the pipe is categorized into three regimes: monotonically increasing, monotonically decreasing, and downward concave profiles. A parametric study indicates that a monotonically decreasing profile appears for a high aspect ratio pipe. A lower aspect ratio pipe, on the other hand, has a monotonically increasing pressure profile. The present paper also reports the effects of the slot width and pressure loss coefficients on the pressure distribution, indicating that the regime of the pressure distribution is mathematically predictable using the function of the design parameters.
The effects of cross flow and fluctuating cross flow on the aerodynamic performance of multirotor drone propellers were investigated by using wind tunnel testing and numerical simulations. Three hovering propellers were examined and were designed based on Adkins and Liebeck theory with modifications. Thrust coefficient CT and power coefficient CP of each propeller were experimentally measured and Figure of Merit FM was evaluated. From the cross flow experiments and numerical simulations, CT, CP and FM calculated were in reasonable agreement with the experimental results at high cross flow velocity. The results implicated that a stall might occur at near the root of the propeller as well as demonstrated that the starting point of the propeller design played a role in aerodynamic performance under the cross flow conditions. Moreover, from the fluctuating cross flow experiments, CT, CP and FM fluctuated in time and the propellers are more susceptible to cross flow and fluctuating cross flow at lower rotational speed in terms of the amount of change of aerodynamic forces.